The Times: can it manage reverses? (6)
I believe the answer is:
epochs
'the times' is the definition.
(both can mean periods in history)
'can it manage reverses?' is the wordplay.
'can it' becomes 'sh' ('can it' can mean stop talking or be quiet).
'manage' becomes 'cope' (synonyms).
'reverses?' is a reversal indicator (I've seen 'reverse of' mean this).
'sh'+'cope'='shcope'
'shcope' in reverse letter order is 'EPOCHS'.
(Other definitions for epochs that I've seen before include "'Periods, eras (6)'" , "dates" , "Remarkable period of time" , "Eras, subdivisions of time" , "Periods of historical time" .)