Wealthy travellers, alien, descended on by NY gang (3,3,3)
I believe the answer is:
the jet set
'wealthy travellers' is the definition.
'alien descended on by ny gang' is the wordplay.
'alien' becomes 'et' (extra terrestrial).
'descended on by' means one lot of letters go next to another (in a down clue, some letters descend onto others).
'ny gang' becomes 'thejets' (the Jets are a gang in West Side Story).
'et' after 'thejets' is 'THE JET SET'.
(Other definitions for the jet set that I've seen before include "frequently found on planes?" , "Wealthy globetrotters" , "Black box" , "on a 747?" .)