Old English cleric leaving clubs (7)
I believe the answer is:
anglian
'old english' is the definition.
(Anglian is an example)
'cleric leaving clubs' is the wordplay.
'cleric' becomes 'anglican'.
'leaving' suggests deleting specific letters.
'clubs' becomes 'c' (abbreviation used in card games such as bridge).
'anglican' with 'c' taken away is 'ANGLIAN'.
(Other definitions for anglian that I've seen before include "Of the tribe from which?England gets its name" , "of German descent" , "English dialect" , "Relating to the Angles" .)