Endeavour to acquire a sleeveless garment for burlesque (8)
I believe the answer is:
travesty
'burlesque' is the definition.
(synonyms)
'endeavour to acquire a sleeveless garment' is the wordplay.
'endeavour' becomes 'try' (synonyms).
'to acquire' means one lot of letters goes inside another.
'sleeveless garment' becomes 'vest' (I've seen this in another clue).
'a'+'vest'='avest'
'try' going around 'avest' is 'TRAVESTY'.
'for' is the link.
(Other definitions for travesty that I've seen before include "Mockery, grotesque imitation" , "Grotesque misrepresentation" , "Vary test (anag.)" , "Farcical imitation" , "Make grotesque" .)