Let's say my Ranger is trying to keep a target at bay, so he uses Ensnaring Strike and hits. On hit, the target is ensnared and must pass a strength save to move.
Now, the question is this:
Is that strength save applied as soon as the target is hit, when it's the targets turn, or both? If both, then does making the save on the target's turn cost its action since it has to make a skill check to get free?
My gut says it's the last point, where the target is forced to burn its action if it wants to get free. Especially since it can opt not to break free and instead just fire a ranged weapon.
Best Answer
For this answer I will use Ensnaring strike as the target example.
Definitely the first one
The save is applied as soon as the target is hit. We can see from the description for Ensnaring strike (PHB 237, emphasis mine):
So, on the same turn that the target is hit, they must make a strength save. If they succeed, then the spell has no effect at all.
If they fail, that brings us to the second part of your question:
As it says in the description for the spell (emphasis mine):
So, if they fail the initial saving throw and are ensnared, someone (either the target or an ally in touch range) must use their action in order to free the target with a Strength check (not a Strength saving throw). Of course, they don't have to use their action breaking free if they don't want to.