Sermon half-abandoned following drink problem (6)
I believe the answer is:
teaser
'problem' is the definition.
(I've seen this before)
'sermon half-abandoned following drink' is the wordplay.
'half-abandoned' means to take half the letters.
'following' means one lot of letters go next to another.
'drink' becomes 'tea' (tea is a kind of drink**).
'sermon' cut in half is 'ser'.
'ser' after 'tea' is 'TEASER'.
(Other definitions for teaser that I've seen before include "Easter (anag) - puzzle" , "A difficult problem of Teresa" , "Introduction to arouse curiosity" , "One who pulls someone's leg" , "one using a backcomb" .)