Edited to undo an Edit 😉

Is there a way within any currently published rules for a cleric to pass themselves off as a cleric of another god?

Or, more to the point, to appear to use the divine gifts (domain abilities) of another cleric?

I have a player who has a great concept for a cleric who serves in an espionage sort of role (perhaps Trickster domain), while posing as, for example, a cleric of Celestian. 

I'd like to help him out, but I'm not sure about any balanced fakery outside illusions or smoke and mirrors style trickery. 

Depends on who you want to fool, and for how long. If you're trying to fool the general population, that's probably fairly easy; if you make your Holy Symbol glow (like with the Light cantrip) and keep a good poker face, the average farmer is likely to believe you're a cleric of the Light God or whatever. Trying to fool other Clerics would be significantly more difficult, but a combination of the Actor and Keen Mind feats could go a long way; Actor would let the character imitate a specific Cleric of another god who they've observed for a minute or longer, and Keen Mind would allow them to perfectly recite passwords or divine secrets they discover in their espionage activities.

Trying to fool other players would only be possible for a short time, particularly if the other players are the types who read very heavily into the sourcebooks. I managed to pass off an Arcane Trickster Rogue as a Wizard for a few sessions with some cleverly allocated Expertises, but I think that's about as long as that kind of joke can last. Eventually someone's going to expect you to be able to do something on the spot that you just can't do, and then the jig will be up.

What if the other god was in on it? Maybe it owed the cleric’s god a favor, or was doing it to test someone, or there was some swap, or they understood it was really for some greater purpose.

Though I guess that’s not within the rules, except how the rules allow the DM to do anything, but I’m thinking that’s not what you meant. In that case, I’d say some deception checks and good old fashioned gaslighting. “Of course I didn’t just throw something at him, it was my light cleric laser beam thingy.”

There is no way for you to use the domain abilities of another domain no. As far as posing for a cleric of a different faith to non clerics that would be entirely up to their proficiency in the relevant skills(deception, performance etc.) as well as having feats that would assist in the process(Keen mind, Observant etc.). 

As far as deceiving other clerics that would be nigh impossible, especially in Faerun.

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I don't want to offend anybody but generally speaking, nobody would know. 

As long as you don't stab them in the back, the party doesn't care who you worship. For the general populace, one cleric is the same as any other unless there is some kind of distinctive uniform or ritual.

Now I'm not saying it's bad idea, just that if I were playing it wouldn't matter a whole lot UNLESS the cleric's endgame was to sacrifice the party to some greater entity.

A trickster cleric still has the cleric spell list which should allow them to pass themselves off as a typical light or healing cleric. They don't need  the channel divinity specifically to perform miracles that look like that of another god. The preserve life spell could easily be replicated  in appearance with something like cure wounds or false life for example.  If you dont like the idea of them actually doing miracles like healing or smiting evil then make the spells illusions with wisdom saving throws replacing saves and attacks or let them make deception checks to hide what they are doing. 

Quote from Wysperra >>

I don't want to offend anybody but generally speaking, nobody would know. 

As long as you don't stab them in the back, the party doesn't care who you worship. For the general populace, one cleric is the same as any other unless there is some kind of distinctive uniform or ritual.

Now I'm not saying it's bad idea, just that if I were playing it wouldn't matter a whole lot UNLESS the cleric's endgame was to sacrifice the party to some greater entity.

 I 100 percent agree this is true of players, but for characters, it’s going to be campaign dependent. A high magic world with lots of capital C clerics running around, and some people are going to know what a given God’s clerics should be able to do. Lower magic worlds or those with fewer clerics, then we’re back to most people not knowing. 

Quote from Xalthu >>

Quote from Wysperra >>

I don't want to offend anybody but generally speaking, nobody would know. 

As long as you don't stab them in the back, the party doesn't care who you worship. For the general populace, one cleric is the same as any other unless there is some kind of distinctive uniform or ritual.

Now I'm not saying it's bad idea, just that if I were playing it wouldn't matter a whole lot UNLESS the cleric's endgame was to sacrifice the party to some greater entity.

 I 100 percent agree this is true of players, but for characters, it’s going to be campaign dependent. A high magic world with lots of capital C clerics running around, and some people are going to know what a given God’s clerics should be able to do. Lower magic worlds or those with fewer clerics, then we’re back to most people not knowing. 

 I don't think I agree that what a cleric should be able to do would be well known because divine powers are ultimately up to gods which are not always clear in their motives or methods and may resent having miracles called on for party tricks or proving a point. 

Just because gods exist doesn't mean people are consistently right or agree about gods and  worship. People in the real world believe they've seen miracles and gods first hand  as well so why would fantasy worlds be any different? 

Some very insightful comments here, thank you!

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EDIT: Please excuse the autocorrected possessive title...grrr

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 Blessings of the pantheon of your choice upon ye! Greatly appreciated.

Quote from Solarsyphon >>

Quote from Xalthu >>

Quote from Wysperra >>

I don't want to offend anybody but generally speaking, nobody would know. 

As long as you don't stab them in the back, the party doesn't care who you worship. For the general populace, one cleric is the same as any other unless there is some kind of distinctive uniform or ritual.

Now I'm not saying it's bad idea, just that if I were playing it wouldn't matter a whole lot UNLESS the cleric's endgame was to sacrifice the party to some greater entity.

 I 100 percent agree this is true of players, but for characters, it’s going to be campaign dependent. A high magic world with lots of capital C clerics running around, and some people are going to know what a given God’s clerics should be able to do. Lower magic worlds or those with fewer clerics, then we’re back to most people not knowing. 

 I don't think I agree that what a cleric should be able to do would be well known because divine powers are ultimately up to gods which are not always clear in their motives or methods and may resent having miracles called on for party tricks or proving a point. 

Just because gods exist doesn't mean people are consistently right or agree about gods and  worship. People in the real world believe they've seen miracles and gods first hand  as well so why would fantasy worlds be any different? 

 That’s why I said campaign dependent. In fact this is an excellent example of it. I get what you’re saying, but other people play differently. 

Quote from Xalthu >>

Quote from Wysperra >>

I don't want to offend anybody but generally speaking, nobody would know. 

As long as you don't stab them in the back, the party doesn't care who you worship. For the general populace, one cleric is the same as any other unless there is some kind of distinctive uniform or ritual.

Now I'm not saying it's bad idea, just that if I were playing it wouldn't matter a whole lot UNLESS the cleric's endgame was to sacrifice the party to some greater entity.

 I 100 percent agree this is true of players, but for characters, it’s going to be campaign dependent. A high magic world with lots of capital C clerics running around, and some people are going to know what a given God’s clerics should be able to do. Lower magic worlds or those with fewer clerics, then we’re back to most people not knowing. 

 Adding on to this, while a high-magic world might have clerics all over the place with clearly defined powers, it's doubtful even in that world that clerics would greet one another by casually showing off their phenomenal cosmic powers. If you run into a Cleric of the Life God on the road and claim to also be a Cleric of the Life God, they're probably not going to say "Oh yeah? Then why don't you turn some Undead right now?!"* More likely they'll quote some scripture at you, maybe throw out a secret handshake or something. The most important things would be these: keep your story straight, know the things you're expected to know, and stay out of situations where you have to practice what they preach.

*Even then, you could just say "Oh, sorry, I already Channeled all my Divinity for the day. Ask me again tomorrow."

So, my initial thought would be how familiar are the average commoners with the symbols of different deities. For example in our world the cross is a pretty ubiqitous symbol of christianity, a Crucifix or rosary being worn would be a pretty big sign that someone is catholic more specifically. In the UK those who belong to the Sikh faith can I believe carry blade that is for religious observance purposes (my apologies to the Sikhs out there I am not familiar with the reason that the item is worn nor what it's actual name is). Such an item is a faith clear identifier that this person belongs to that faith.

Carrying that over to a fantasy setting, yes the possibilities are endless but I'm slightly old school and as such see Clerics and Paladins as faith/religion based. I would think that there would be some signifiers of the faith to which you porport to belong. The most obvious of these would be the holy symbol. Now here's where the rules as written open the door to what you're asking - the rules just say a cleric can use a holy symbol - there's no specification that it must be of the deity or religion to whom they belong. Personal opinion here would be that a cleric of Lathandar carrying and utilising a holy symbol of Sune might be considered in some way blasphemous and I might work some story stuff around that, but there is no reason your world has to work that way. You can choose for it to work however you wish. 

Maybe, the cleric in question might wear the robes and ceremonial clothing of Sune, but their holy symbol might be of Lathandar. I can't necesserily see an issue with that. 

The only other caveat here is if you place any import or stock in alignment. That might affect such a cleric. If their deity/religion place import on honour or truth or law, that might also be a problem for the deceptive cleric.

Either way I can see it as a really interesting way to craft a story - especially if said cleric player is willing to put up with maybe some curveballs as a result of appearing to represent a different deity.