George is happy - but not completely - with a Japanese entertainer (6)
I believe the answer is:
geisha
'a japanese entertainer' is the definition.
(geishas traditionally hosted or entertained men)
'george is happy but not completely' is the wordplay.
'not completely' indicates the answer is hidden within the clue.
'GEISHA' is hidden in the letters of 'george is happy but'.
'with' is the link.
(Other definitions for geisha that I've seen before include "One employed to look after men" , "Japanese woman trained to please men" , "Entertainer in a kimono?" , "He's a GI (anag.)" , "Entertaining girl" .)