Slept so bust is half-naked (7)
I believe the answer is:
topless
'half-naked' is the definition.
(I've seen this before)
'slept so bust' is the wordplay.
'bust' is an anagram indicator.
'slept'+'so'='sleptso'
'sleptso' anagrammed gives 'TOPLESS'.
'is' is the link.
(Other definitions for topless that I've seen before include "As a Page Three girl?" , "Without a shirt, vest or bra?" , "Naked above the waist" , "Bare from the waist up" , "Half naked" .)