Carries on with The Times (5)
I believe the answer is:
wages
'carries on' is the definition.
(as in waging war)
'with the times' is the wordplay.
'with' becomes 'w' (abbreviation).
'the times' becomes 'ages' (age is a kind of time).
'w'+'ages'='WAGES'
(Other definitions for wages that I've seen before include "Work pay" , "Earnings for work - or of sin" , "Weekly pay" , "Salaries" , "Worker's earnings" .)