Life jacket may make me sweat (3,4)
I believe the answer is:
mae west
'life jacket' is the definition.
(Mae West is an example)
'make me sweat' is the wordplay.
'make' indicates anagramming the letters.
'me'+'sweat'='mesweat'
'mesweat' anagrammed gives 'MAE WEST'.
'may' is the link.
(Other definitions for mae west that I've seen before include "Source of innuendos" , "I acted" , "jacket found floating in the sea" , "life-saver" , "Ex-player" .)