Got rid of a female deadhead (4)
I believe the answer is:
shed
'got rid of' is the definition.
'a female deadhead' is the wordplay.
'a female' becomes 'she' (I've seen this before**).
'deadhead' becomes 'd' (head letter of 'dead').
'she'+'d'='SHED'
(Other definitions for shed that I've seen before include "storage unit" , "lost" , "Lose as trees do leaves" , "One-storeyed outbuilding" , "In which lawnmower is kept" .)