I would like to comment that adding 3 new fish at the same time in a lightly stocked tank invites a new mini-cycle. That is, before adding the new fish, the tank was in equilibrium with its current bio-load. In your case, 4 small fish. You then added 3 new fish, essentially doubling the bio-load. It takes some time for the bacteria population to grow and meet the new demand, which will possibly allow the ammonia and nitrite levels to rise. The bottom line is that you should go easy on adding fish maybe only adding 1 or at worst 2 at a time. Of course, once you have a bunch of larger fish, say 10, adding a new fish or two will only increase the bio load by 10-20%, much easier for the tank to recover from the change.
That being said, wrasses can and do hide a lot at first when being introduced to a new tank. Plus they often come from around the world, and may not be on the same time schedule as your tank (jet-lagged) and it takes time for them to adjust. So I would say that your wrasse may well be fine, give it some time, and best of luck.