Posh doctor involved in Royal Academy dance (5)
I believe the answer is:
rumba
'dance' is the definition.
(rumba is a type of dance)
'posh doctor involved in royal academy' is the wordplay.
'posh' becomes 'u' (abbreviation for upper-class - opposite to non-U).
'doctor' becomes 'MB' (Bachelor of Medicine, Medicinae Baccalaureus).
'involved in' is an insertion indicator.
'royal academy' becomes 'RA'.
'u'+'mb'='umb'
'umb' inserted inside 'ra' is 'RUMBA'.
(Other definitions for rumba that I've seen before include "Rhythmic dance of Cuban origin" , "Umbra (anag)" , "Style of dance" , "music one can dance to" , "number of steps" .)