Mention judge with hesitation (5)
I believe the answer is:
refer
'mention' is the definition.
(I know that mention can be written as refer)
'judge with hesitation' is the wordplay.
'judge' becomes 'ref' (referee).
'with' is a charade indicator (letters next to each other).
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'ref'+'er'='REFER'
(Other definitions for refer that I've seen before include "Fail (an exam candidate)" , "Consult" , "Draw attention" , "Make allusion, direct attention with words" , "Allude, assign" .)