Drink beginning to excite religious leader (4)
I believe the answer is:
pope
'religious leader' is the definition.
(I know that pope is a type of bishop)
'drink beginning to excite' is the wordplay.
'drink' becomes 'pop' (pop is a kind of drink).
'beginning to' suggests taking the first letters.
The first letter of 'excite' is 'e'.
'pop'+'e'='POPE'
(Other definitions for pope that I've seen before include "Head of Roman Catholic Church" , "Top bishop" , "Francis < Alexander" , "English poet, d. 1744" , "Satirist" .)