Started, for instance, during prohibition (5)
I believe the answer is:
'started' is the definition.
('begin' can be a synonym of 'start')
'for instance during prohibition' is the wordplay.
'for instance' becomes 'eg' ('e.g.' can be a synonym of 'for instance'**).
'during' indicates putting letters inside.
'prohibition' becomes 'ban' (ban is a kind of prohibition).
'eg' put inside 'ban' is 'BEGAN'.
(Another definition for began that I've seen is " Commenced, started".)