New remit for headgear (5)
I believe the answer is:
mitre
'for headgear' is the definition.
(mitre is a kind of headgear)
'new remit' is the wordplay.
'new' is an anagram indicator.
'remit' is an anagram of 'MITRE'.
(Other definitions for mitre that I've seen before include "One identifies bishop" , "Corner joint - bishop's headdress" , "Episcopal headdress" , "Corner joint - bishop's hat" , "Timer for a bishop." .)