Deal with a day shift? (7)
I believe the answer is:
address
'deal with' is the definition.
('address' can be a synonym of 'deal with')
'a day shift?' is the wordplay.
'a day' becomes 'ad' (I've seen this in other clues).
'shift?' becomes 'dress' (shift is a kind of dress**).
'ad'+'dress'='ADDRESS'
(Other definitions for address that I've seen before include "Give a speech to" , "Speak formally to an audience" , "Attend" , "Speech; one's home" , "Talk - indication of house" .)