Big band has rector dancing (9)
I believe the answer is:
orchestra
'big band' is the definition.
'has rector dancing' is the wordplay.
'dancing' indicates anagramming the letters.
'has'+'rector'='hasrector'
'hasrector' anagrammed gives 'ORCHESTRA'.
(Other definitions for orchestra that I've seen before include "Large musical group" , "Eg, LSO, RPO" , "Noted performers" , "Large band of players" , "Group of musical instrumentalists" .)