Man put out about recollection of my crucial part in hearing (8)
I believe the answer is:
tympanum
'crucial part in hearing' is the definition.
(part of the ear)
'man put out about recollection of my' is the wordplay.
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'about' indicates putting letters inside.
'recollection of' says the letters should be written backwards (recollect letters in the opposite direction).
'my' reversed gives 'ym'.
'man'+'put'='manput'
'manput' with letters rearranged gives 'tpanum'.
'tpanum' enclosing 'ym' is 'TYMPANUM'.
(Other definitions for tympanum that I've seen before include "Eardrum" , "drum" , "Ear membrane -- my MP a nut (anag)" , "Cavity of the middle ear" .)