I agree with the above, changing around the rockwork usually helps.
How large is the tank? Is there room for both to have territory? As a side note, I have found fairy wrasses to be somewhat skittish to begin with, they seem to let other fish take advantage of them lol. But letting him get comfortable in the new tank will def help as well.
is there a large size disparity between the two fish? I can def see a very small fairy getting the short end of the tang stick hehe...But it really should calm down in a few days. I've only ever had to remove fish one time, a pair of clowns that were in a 125g with another pair of clowns so I knew going in that it night be a bad thing. But tangs typically will harass any new addition, even other tangs or fish larger than them.
180g Reef - 60g Rimless Reef -90G FOWLR- 125g Malawi Cichlids- 40b REEF- 34g Fresh Planted-working on- 20L FOWLR- working on
I have a mix of many different saltwater fish amongst my tanks, but I love my Tangs most of all.