Can you shift your target lock from one ship to another as an action?

Yes.

Edit: (This is assuming you mean you have a ship which has a prior TL on an enemy ship, now you want to take the TL action on a different enemy ship within range. Yes, you would essentially remove the old TL and put a new one on a different ship within range)

Technically you discard the existing TL and acquire a new one.

Technically you discard the existing TL and acquire a new one.

What you can't do is relock the same ship that's you've already got a lock on. There's only a few cases where you'd want to do that since you'd be using an action to get a target lock that you've already got. There are a couple of cards that have acquiring a target lock as a a trigger.