Possibly battier accessory for father (7)
I believe the answer is:
biretta
'accessory for father' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.
'possibly battier' is the wordplay.
'possibly' indicates anagramming the letters.
'battier' anagrammed gives 'BIRETTA'.
Can you help me to learn more?
(Other definitions for biretta that I've seen before include "Cloth cap" , "Cardinal's red cap" , "Roman Catholic priest's cap" , "Clergyman's cap" , "Square cap worn by Roman Catholic clergy" .)