Currently a level 8 pact of the chain warlock with investment of the chain master, can my imp attack on his turn or can he only attack during my turn with my bonus action?
You learn the find familiar spell and can cast it as a ritual. The spell doesn’t count against your number of spells known.When you cast the spell, you can choose one of the normal forms for your familiar or one of the following special forms: imp, pseudodragon, quasit, or sprite.Additionally, when you take the Attack action, you can forgo one of your own attacks to allow your familiar to make one attack with its reaction.
So...YOU must give up one of your attack actions to have your imp attack instead. A terrible idea, IMHO. But then...in my personal opinion, using your familiar to attack is a bad idea under almost all circumstances. Attacking is simply not what you should be using your familiar for. Again, just my opinion, many would disagree. But your familiar is far too delicate for combat, and familiar attacks just clog up the action economy and slow the game for everyone. Lastly, familiar attacks are very weak in all but the most situational circumstances. It is hard to imagine how a good old Eldritch Blast would not be a better option. If you MUST have your familiar enter the fray, try having your imp use the Help action to grant you advantage on one of your attacks instead.
Now, once you get Investment of the Chain Master, then you can use your bonus action to tell your imp to attack. Which is still a bad idea, IMHO. I would pick a different invocation and skip Investment of the Chain Master (there are many better Invocations).
Investment of the Chain Master
Prerequisite: Pact of the Chain feature When you cast find familiar, you infuse the summoned familiar with a measure of your eldritch power, granting the creature the following benefits:
The familiar gains either a flying speed or a swimming speed (your choice) of 40 feet.
As a bonus action, you can command the familiar to take the Attack action.
The familiar’s weapon attacks are considered magical for the purpose of overcoming immunity and resistance to nonmagical attacks.
If the familiar forces a creature to make a saving throw, it uses your spell save DC.
When the familiar takes damage, you can use your reaction to grant it resistance against that damage.
Currently a level 8 pact of the chain warlock with investment of the chain master, can my imp attack on his turn or can he only attack during my turn with my bonus action?
Here are the current rules (UA is different)
Pact of the Chain
You learn the find familiar spell and can cast it as a ritual. The spell doesn’t count against your number of spells known.When you cast the spell, you can choose one of the normal forms for your familiar or one of the following special forms: imp, pseudodragon, quasit, or sprite.Additionally, when you take the Attack action, you can forgo one of your own attacks to allow your familiar to make one attack with its reaction.
So...YOU must give up one of your attack actions to have your imp attack instead. A terrible idea, IMHO. But then...in my personal opinion, using your familiar to attack is a bad idea under almost all circumstances. Attacking is simply not what you should be using your familiar for. Again, just my opinion, many would disagree. But your familiar is far too delicate for combat, and familiar attacks just clog up the action economy and slow the game for everyone. Lastly, familiar attacks are very weak in all but the most situational circumstances. It is hard to imagine how a good old Eldritch Blast would not be a better option. If you MUST have your familiar enter the fray, try having your imp use the Help action to grant you advantage on one of your attacks instead.
Now, once you get Investment of the Chain Master, then you can use your bonus action to tell your imp to attack. Which is still a bad idea, IMHO. I would pick a different invocation and skip Investment of the Chain Master (there are many better Invocations).
Investment of the Chain Master
Prerequisite: Pact of the Chain feature
When you cast find familiar, you infuse the summoned familiar with a measure of your eldritch power, granting the creature the following benefits:
Nathair Sgiathach is my co-pilot