You might get more specific help by posting in the Anemones & clownfish area. But in general you should give your new tank some time to stabilize - maybe a week or 2, depending on whether you move all your sand & water from the old tank, which I'd recommend, before adding new fish
Pink skunks aren't that aggressive & are a very good choice for a small sized tank, I might add. If it was me - I'd find one that is about 1/2 (or less) the length of the existing fish & add it at the same time as the new anemone (which I assume you have correct lighting for). I would also make sure that the new addition is a juvenile & definitely not a female. All this is assuming your existing fish is a female which it most likely it is if you've had it a while.