Professorship of Prosthetic Hairdressing (5)
I believe the answer is:
'professorship' is the definition.
'of prosthetic hairdressing' is the wordplay.
'of' indicates a hidden word.
'CHAIR' can be found hidden inside 'prosthetic hairdressing'.
(Other definitions for chair that I've seen before include "Preside over - seat" , "conduct" , "Presiding officer" , "president" , "academic office" .)