A new campaign is coming up for the new year. Was wondering if a Variant Aasimar monk cleric multiclass would work, and not suck? I plan to go mainly into monk, but also a decent amount of levels in cleric? I will be using life cleric, and either open hand or a homebrew subclass I’m working on, called, way of the sacred tome. The campaign is based off the TV show Loki, so flavour wise it seems great. Just wanna know if it is mechanically sound at 3 areas:

1. Support
2. Damage
3. Versatility

Thanks

It’s going to be impossible to say without details on the subclass. 
That said, the first thing that comes to mind is life clerics get heavy armor, and you won’t be wearing that, so you’ll miss out on a subclass feature. 
But spirit guardians and punching someone seems a nifty combo. And you’ll have a good wisdom, so your monk save DCs will be pretty high. Stunning someone in your spirit guardians will be sweet. But you won’t have that until level 10 at the earliest.
I’d just watch your bonus action economy. Flurry of blows, and a number of other monk powers are BAs, and healing word is a BA. So you could wind up with situations where they’re competing. And you’ll pretty much never use spiritual weapon. I’d take a careful look at the spell list and see how many other spells you’ll lose out on. 

If it were me I would likely pick any cleric subclass other than Life, as it really brings relatively little to the table under the best of circumstances. For a more “Loki” themed build I would probably go with Trickery, it’ll probably synergize better with Monk in general too.

I had a player create a cleric/monk build and it was awful; they spent the entire time complaining about how ineffective they were until I pasted a magic item over the gaping hole they made for themselves. It certainly can be fun to build it, but you can very easily create a problem for yourself.

This player started as a Tempest Cleric for the lightning powers, but they aren't that impressive alone, hence the armor and weapons proficiency. The problem with that is that a monk dip after that is going to be a little underwhelming if you want to be a punch kicky fighter, while your ability with weapons is going to simply be better. You also won't get to use monk features that require an absence of armor OR a shield.

So at the very least, avoid the Tempest subclass unless you are fine not using a lot of monk features or some Tempest features.

Quote from Erik_Soong >>

I had a player create a cleric/monk build and it was awful; they spent the entire time complaining about how ineffective they were until I pasted a magic item over the gaping hole they made for themselves. It certainly can be fun to build it, but you can very easily create a problem for yourself.

This player started as a Tempest Cleric for the lightning powers, but they aren't that impressive alone, hence the armor and weapons proficiency. The problem with that is that a monk dip after that is going to be a little underwhelming if you want to be a punch kicky fighter, while your ability with weapons is going to simply be better. You also won't get to use monk features that require an absence of armor OR a shield.

So at the very least, avoid the Tempest subclass unless you are fine not using a lot of monk features or some Tempest features.

 What was the hole in their build? I have just made a test version of a monk cleric and it will go god mode

The hole in the build that my player used was that there no synergy in anything they wanted to do. If you wear the armor that the Tempest gives you, you can't use martial arts. If you want to use martial arts, you can't use martial weapons because you invest in Dex. If you choose to invest in Str so you can use your martial weapons and unarmed strikes, you can't use unarmored defense or deflect missiles or any other monk feature that uses dex. It just didn't do anything very well and absolutely failed to meet the player's needs. I do think you can make a cleric/monk build work, but it will absolutely come down to the subclasses, as Xalthu said.

On top of all this, the party will need a healer and the more you dip into monk, the less you can function in that capacity. So it would be a good idea to make sure there is a main healer because if you are mostly going monk and do not plan to be a Mercy Monk, you won't fill that role very well.

The multiclass is good, but you need to know what you are going for and there will be limitations.  You can't just flip flop cleric/monk levels and be successful.  You will generally need to take one of these to 5th level (with at best a 1 level dip in the other mostly for flavor) before balancing yourself later.  5th level for both classes with extra attack and spirit guardians is a very large step up and power.  A 5/5 balanced build is quite good... but you need to solve a few issues:
1. Concentration.  You don't have a good way to maintain a spell and you are absolutely going to get hit.  Since spirit guardians does damage at the beginning of their turn it is very advantageous to hit the spellcaster before more enemys take their turn.  If this is your build you need to protect it concentration more than just about any other ability.  You only have so many ASI's.  
2. Armor Class.  The fact monks can't use shields is so very, very frustrating here.  With unarmored defense you are starting at 16.  The cleric route will have a slightly better AC because a shield is great, but as soon as you want to use some of the monk toys you are back down.  If you can pull the shield spell you can help yourself out.  Otherwise variant human/custom lineage can get you either defensive duelist or gift of the metallic dragon.
3. You can't be the only healer.  No party should have only one healer anyway.  Spread that out around the party.  More critically you need someone with greater restoration.  Make sure someone is getting it (Druid or Bard). 
Are there less than 50/50 builds that are useful.  Yes.  Bless is great on a monk.  Monk plus 3 levels of cleric is not bad.  6 spells per long rest is really nice and that bump from 3 spells to 6 going from 2 to 3rd level in Cleric is a big deal.  There are plenty of good 1st and 2nd level spells, and bless is a good spell until the end of your days.  It also helps that the bless helps maintain the bless.  I am not sure there is a reason to do a 1 level dip into monk unless you really want to play up an unarmored spell casting fantasy.

This multiclass will improve a Monk after they get 5 levels in, but will generally make a Cleric a lot worse. Despite what the person above said, it is generally a bad multiclass.

Cleric is a great class that already has a ton of versatility.

What are you trying to gain from Monk to make this multiclass worthwhile? Monk does not multiclass well because of how Ki starved they all and how their features do not play well with armor, shields, or martial weapons.

Monk is generally bad for multi-classing due to Unarmored Movement, Martial Arts and Unarmored Defense, all of which mean you cannot use Armor or a Shield. Unless you roll and get very high starting stats, it will be difficult to survive more than a round of combat in many cases using Aasimar as your base since they provide no AC bonus.  While you get resistance to two types of damage (Necro and Radiant), basic bludgeoning, piercing,  and slashing are still the most common in most encounters. While the Radiant damage done by the Aasimar is attractive, staying alive to do that damage remains crucial.

Instead of Aasimar, consider the Tortle.  Their shell grants them a much better (17) base AC so that having a high DEX is far less of a priority. With Tasha's rules, you can change around the stat bonuses to where you want them. 

If you don't mind restricting yourself to the Kensei subclass for Monk you could maybe get away with a Lizardfolk or Thri-Kreen Monk, since both give you 13 base AC before even looking at Unarmored Defense. The reason is that the Agile Parry feature of the Kensei gives you a static +2 to AC as long as you attack with an unarmed strike while wielding a weapon that you "mark" using their Kensei ability.

However, Tortle is still better overall since your choice of Life Cleric really means you want to spend a lot of your actions or bonus actions healing, amiright?  In that case there's really no better choice than Mercy Monk, who can heal w/out spending additional Ki points just by doing their typical Flurry of Blows. You also get the opportunity to inflict Poisoned condition on enemies using your Flurries, which meshes very well with Spirit Guardians' slowing of movement. 

Note the new Unearthed Arcana rules for monks allow them to use the bonus Unarmed strike attack without it being tied to an attack action.  This means you could cast a spell and flurry of blow or unarmed strike in the same turn, and makes this class combination more useful.

UA rules don't mean anything to most tables until they get published as official rules.

Quote from Song_of_Blues>>

Monk is generally bad for multi-classing due to Unarmored Movement, Martial Arts and Unarmored Defense, all of which mean you cannot use Armor or a Shield.

I don't really see how these two things are related; if you're planning to go a multiclass involving Monk then it means you want to be playing unarmored, otherwise why would you do it?

Personally I've found Cleric and Monk pair extremely well, but you have to be very careful about when you do it; in general you're better off starting as Monk since it'll be determining the gear you can actually use, and has the boosts to counter the lack of armour. But a Monk doesn't want to multiclass too soon, as you're very Ki dependent early on, and anything that delays Extra Attack will really hurt your combat performance. This is part of why you don't want to start as a Cleric.

I played a Monk/Cleric starting at 3rd-level with two levels in Monk and one in Cleric, but I wouldn't do that split again. While Cleric being very front-loaded can give a lot of good benefits, it does mean delaying a lot of good Monk stuff at the same time. So while I had cantrips, a handful of spells and some 1st-level domain benefits, I also didn't have Deflect Missiles or a sub-class at the start, and as the campaign progressed this delay remained an issue until I finally reached the Monk 7/Cleric 3 mark. By this point you also have a good working amount of Ki and a lot of good Monk benefits already, and what you're getting out of Cleric is more than worth the three less Ki points.

For this reason I don't recommend starting with Cleric, and you don't want to split until you've got at least five levels in Monk, though this depends on the sub-class as 6th-level is very good for some, and once you grab that you might as well get 7th-level for Evasion. Most Cleric domains give pretty good benefits just for a single level, so if you do dip early you need to keep that Cleric level low and resist the temptation to grab 2nd-level for Channel Divinity, because once you do you'll just be tempted to take a 3rd Cleric level for 2nd-level spells.

So yeah, it's a great combo IMO, but one you really need to be aware of the balancing act for. It's not really unique to Monk as when to split is a problem common to all multi-classing, the armour to no-armour transition is unique to Monk but it's not like it's a surprise.