My man put off drum (8)
I believe the answer is:
tympanum
'drum' is the definition.
(thesaurus)
'my man put off' is the wordplay.
'off' indicates anagramming the letters.
'my'+'man'+'put'='mymanput'
'mymanput' with letters rearranged gives 'TYMPANUM'.
(Other definitions for tympanum that I've seen before include "Ear membrane -- my MP a nut (anag)" , "Cavity of the middle ear" , "drum" , "Eardrum" .)