Rhythm of dance organised in outskirts of Carlisle (7)
I believe the answer is:
cadence
'rhythm' is the definition.
(cadence is a kind of rhythm)
'dance organised in outskirts of carlisle' is the wordplay.
'organised' is an anagram indicator.
'in' indicates putting letters inside.
'outskirts of' says to hollow out the word (remove centre letters).
'carlisle' with its middle removed is 'ce'.
'dance' anagrammed gives 'adenc'.
'adenc' inserted within 'ce' is 'CADENCE'.
'of' acts as a link.
(Other definitions for cadence that I've seen before include "Rise and fall" , "Closing bars" , "that may be perfect for musicians" , "Rhythm or beat" , "Vocal modulation or inflection" .)