Remove one's used sweaty tank tops (4)
I believe the answer is:
oust
'remove' is the definition.
(ousting is a kind of removing)
'one's used sweaty tank tops' is the wordplay.
'tops' indicates taking the first letters.
The first letters of 'ones used sweaty tank' is 'OUST'.
(Other definitions for oust that I've seen before include "Expel - eject" , "Get rid of" , "Remove and replace" , "kick out" , "Depose" .)