Cycle briefly in island bomb site
I believe the answer is:
bikini
'bomb site' is the definition.
(I've seen this before)
'cycle briefly in island' is the wordplay.
'cycle' becomes 'bike' (bike is a kind of cycle).
'briefly' means to remove the last letter.
'island' becomes 'i'.
'bike' with its final letter taken off is 'bik'.
'bik'+'in'+'i'='BIKINI'
(Other definitions for bikini that I've seen before include "Skimpy two-piece swimsuit" , "Atoll and swimming costume" , "Minuscule bathing costume for woman" , "providing little cover for swimmers" , "Small two-piece bathing suit" .)