Muslim more cheerful, without hesitation (5)
I believe the answer is:
sunni
'muslim' is the definition.
(Sunni is an example)
'more cheerful without hesitation' is the wordplay.
'more cheerful' becomes 'sunnier' ('sunny' can be similar in meaning to 'cheerful').
'without' suggests deleting specific letters.
'hesitation' becomes 'er'.
'sunnier' with 'er' taken out is 'SUNNI'.
(Other definitions for sunni that I've seen before include "Moslem" , "Islamic faction" , "Indian fig tree with aerial roots" , "Member of another Muslim sect" , "One branch of Islam" .)