Dancing permitted by graduate student? (6)
I believe the answer is:
ballet
'dancing' is the definition.
(ballet is a kind of dancing)
'permitted by graduate student?' is the wordplay.
'permitted' becomes 'let' (I've seen this before).
'by' means one lot of letters go next to another.
'graduate' becomes 'ba' (**).
'student?' becomes 'l' (as in L-plates for learner drivers).
'ba'+'l'='bal'
'let' put after 'bal' is 'BALLET'.
(Other definitions for ballet that I've seen before include "The theatre of dance" , "Artistic dance form" , "Dance entertainment" , "kind of skirt" , "old madrigal" .)