Time to manage flipping hours (5)
I believe the answer is:
epoch
'time' is the definition.
(epoch is a kind of time)
'manage flipping hours' is the wordplay.
'manage' becomes 'cope' (manage can mean to cope or do well).
'flipping' says the letters should be written backwards.
'hours' becomes 'h'.
'cope' backwards is 'epoc'.
'epoc'+'h'='EPOCH'
'to' acts as a link.
(Other definitions for epoch that I've seen before include "remarkable time" , "significant time" , "A particular period of history" , "Particular historic time period" , "Distinctive period of time" .)