Shag and doze off (3)
I believe the answer is:
nap
This clue is a double definition.
'shag' is the first definition.
(thesaurus)
'doze off' is the second definition.
'and' is the link.
(Other definitions for nap that I've seen before include "Sleep - card game - fibres on a snooker table" , "A brief sleep, forty winks" , "Racing tip that professes to be a certainty" , "Short sleep on fuzzy fabric surface" , "A brief informal sleep" .)