British head of church absorbed by such a dissolute god (7)
I believe the answer is:
bacchus
'god' is the definition.
(Bacchus is an example)
'british head of church absorbed by such a dissolute' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'head of' indicates taking the first letters.
'absorbed by' is an insertion indicator.
'dissolute' is an anagram indicator.
The first letter of 'church' is 'c'.
'such'+'a'='sucha'
'sucha' with letters rearranged gives 'achus'.
'c' going into 'achus' is 'acchus'.
'b'+'acchus'='BACCHUS'
(Other definitions for bacchus that I've seen before include "Greek god of boozing" , "Greek god of drink, also called Dionysus" , "Greek god of booze" , "Roman god of drink and revelry" , "Another name for Dionysus, Greek god of drink" .)