A day off for Billie (7)
I believe the answer is:
holiday
I believe this clue is a double definition.
'a day off' is the first definition.
(thesaurus)
'billie' is the second definition.
(I've seen this before)
'for' is the link.
(Other definitions for holiday that I've seen before include "Time off work" , "- leave" , "jazz singer" , "Day of festivity" , "rest" .)