Swimsuits composer carried across East River (9)
I believe the answer is:
beachwear
'swimsuits' is the definition.
(items worn at the beach)
'composer carried across east river' is the wordplay.
'composer' becomes 'bach' (Bach is an example).
'carried across' means one lot of letters goes inside another.
'east' becomes 'e' (synonyms).
'river' becomes 'wear' (river in the north east of England).
'bach' going around 'e' is 'beach'.
'beach'+'wear'='BEACHWEAR'
(Other definitions for beachwear that I've seen before include "Bikini, for instance" , "skimpy garments" , "Speedos for one" , "Holiday clothing" , "Trunks, bikinis etc" .)