Unaccompanied singing in palace -- with lap dancing! (1,8)
I believe the answer is:
a cappella
'unaccompanied singing' is the definition.
(I've seen this before)
'palace with lap dancing' is the wordplay.
'with' is a charade indicator (letters next to each other).
'dancing' indicates an anagram.
'palace'+'lap'='palacelap'
'palacelap' anagrammed gives 'A CAPPELLA'.
'in' acts as a link.
(Other definitions for a cappella that I've seen before include "Sung without instrumental accompaniment" , "type of singing" , "Palace pal singing without musical accompaniment" , "Of choral music, unaccompanied" , "Palace pal in unaccompanied song" .)