Has to dishearten Tony, quick! (5)
I believe the answer is:
hasty
'quick' is the definition.
(I've seen this before)
'has to dishearten tony' is the wordplay.
'to dishearten' suggests removing the centre.
'tony' with its centre removed is 'ty'.
'has'+'ty'='HASTY'
(Other definitions for hasty that I've seen before include "Impulsive" , "Hurried; without thinking" , "Precipitous" , "Too hurried, careless" , "Quick but ill-considered" .)