Kills time: then prescribes first time must be forgotten (10)

'kills' is the definition.
(to eradicate is to kill or destroy)

'time then prescribes first time must be forgotten' is the wordplay.
'time' becomes 'era' (era is a kind of time).
'then' is a charade indicator (letters next to each other).
'prescribes' becomes 'dictates' ('dictate' can be a synonym of 'prescribe').
'first time' becomes 't' (1st letter of 'time').
'must be forgotten' indicates named letters should be taken away.
'dictates' with 't' removed is 'dicates'.
'era'+'dicates'='ERADICATES'