Most recent time after evening shifts (6)
I believe the answer is:
latest
'most recent' is the definition.
('late' can be similar in meaning to 'recent')
'time after evening shifts' is the wordplay.
'time' becomes 't'.
'after' is a charade indicator (letters next to each other).
'evening shifts' becomes 'lates'.
't' put after 'lates' is 'LATEST'.
(Other definitions for latest that I've seen before include "Stop press news?" , "Most recent (news)" , "Of most recent date" , "News update" , "Most recent or most unpunctual" .)