Late shift perhaps in close connection (7)
I believe the answer is:
nightie
'late shift perhaps' is the definition.
(I've seen this before)
'close connection' is the wordplay.
'close' becomes 'nigh' (similar in meaning).
'connection' becomes 'tie' (tie is a kind of connection).
'nigh'+'tie'='NIGHTIE'
'in' is the link.
(Other definitions for nightie that I've seen before include "Loose garment" , "Coverage for the rest" , "one put on after dark" , "covering for retired person" , "Garment for ladies" .)