Partly deaf, terribly behind (5)
I believe the answer is:
after
'behind' is the definition.
(eg after or behind someone in a queue)
'partly deaf terribly' is the wordplay.
'partly' indicates a hidden word (part of the clue is used).
'AFTER' is hidden in the letters of 'deaf terribly'.
(Other definitions for after that I've seen before include "Coming later in time" , "In the time following" , "Following - behind" , "Behind; in quest of" , "Following, consequent to" .)