"Each of your turns" Gathered swarm clarification

Question

I'm trying to figure out if I can do the reaction polearm master and use gathered swarm if I hit

I'm just honestly confused by the "each of your turns" part of gathered swarm.

Answer 1

Only during your turn

The Gathered Swarm feature says:

Once on each of your turns, you can cause the swarm to assist you in one of the following ways, immediately after you hit a creature with an attack

So you can only use it on your own turn. Wether you use it through a reaction or a normal action. What counts is that it is only once, only on your turn, and only when you hit a creature with an attack.

The polearm master feat says

• While you are wielding a glaive, halberd, pike, quarterstaff, or spear, other creatures provoke an opportunity attack from you when they enter the reach you have with that weapon.

So, you are just making an opportunity attack using your Reaction. You also could make one as usual, if someone leaves your reach. It does not matter. What matters is when you make it.

Most of the time, creatures move during their own turn, so most of the time you'd make this during another creatures turn, not your turn, and would be unable to use Gathered Swarm.

However, if someone took a Ready action to move on your turn, using their own Reaction, and moved within your reach, then you could use Polearm Master to make an opportunity attack, and if you hit, you could use Gathered Swarm.