Father possibly angry giving up house (6)
I believe the answer is:
cleric
'father possibly' is the definition.
(I know that Father is a type of Priest)
'angry giving up house' is the wordplay.
'angry' becomes 'choleric' (choleric means angry or bad-tempered).
'giving up' indicates named letters should be taken away.
'house' becomes 'ho' (abbreviation for house).
'choleric' with 'ho' taken away is 'CLERIC'.
(Other definitions for cleric that I've seen before include "Religious man" , "Person in holy orders" , "One is in religious orders" , "Type of cloth, perhaps" , "Church official" .)