Rhythm of new dance in church (7)
I believe the answer is:
cadence
'rhythm' is the definition.
(cadence is a kind of rhythm)
'new dance in church' is the wordplay.
'new' is an anagram indicator.
'in' is an insertion indicator.
'church' becomes 'CE' (abbreviation for Church of England).
'dance' is an anagram of 'adenc'.
'adenc' going inside 'ce' is 'CADENCE'.
'of' acts as a link.
(Other definitions for cadence that I've seen before include "Rhythm or beat" , "Tonal inflection" , "Close of a musical phrase" , "Closing bars" , "Rise and fall" .)