Started with a bang, perhaps, around mid-September (5)

I believe the answer is:

began

'started' is the definition.
('begin' can be a synonym of 'start')

'a bang perhaps around mid-september' is the wordplay.
'perhaps' indicates an anagram.
'around' is an insertion indicator.
'mid' says to take the centre.
'september' becomes 'sep' (short for September).
The middle of 'sep' is 'e'.
'bang' is an anagram of 'bgan'.
'bgan' going around 'e' is 'BEGAN'.

'with' acts as a link.

(Another definition for began that I've seen is " Commenced, started".)

I've seen this clue in the Evening Standard.

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