Minister reduced by hack’s comic verse (8)
I believe the answer is:
clerihew
'comic verse' is the definition.
(type of humorous four-line poem)
'minister reduced by hack's' is the wordplay.
'minister' becomes 'cleric' (I've seen this before).
'reduced' means to remove the last letter.
'by hack' becomes 'hew' (I've seen this before. I am not sure about the 'by' bit.).
'cleric' with its last letter removed is 'cleri'.
'cleri'+'hew'='CLERIHEW'
(Other definitions for clerihew that I've seen before include "E.C.Bentley's verse form" , "Bentley's jingle" , "few personal lines" , "Short comic verse form" , "Satire of rhymed couplets about a famous person" .)