Church's first dance is cut (4)
I believe the answer is:
chop
'cut' is the definition.
(chop is a kind of cut)
'church's first dance' is the wordplay.
'first' indicates taking the first letters.
'dance' becomes 'hop' (hop is a kind of dance).
The first letter of 'churchs' is 'c'.
'c'+'hop'='CHOP'
'is' acts as a link.
(Other definitions for chop that I've seen before include "Hew" , "Cut - a piece of meat" , "mutton slice" , "Reduce drastically" , "Small cut of meat" .)