Dance around with extremely close rhythm (7)
I believe the answer is:
cadence
'rhythm' is the definition.
(cadence is a kind of rhythm)
'dance around with extremely close' is the wordplay.
'around with' indicates anagramming the letters.
'extremely' says to hollow out the word (remove centre letters) (only the extremes of the word are used).
'close' with its middle removed is 'ce'.
'dance' mixed up with 'ce' gives 'CADENCE'.
(Other definitions for cadence that I've seen before include "Lilt" , "Rhythm or beat" , "Inflection; voice pitch fall" , "Tonal inflection" , "Closing bars" .)