Is worn, having influence no longer (8)

I believe the answer is:

pullover

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'is worn' is the definition.
I can't judge whether this definition defines the answer.

'influence no longer' is the wordplay.
'influence' becomes 'pull' (I've seen this before).
'no longer' becomes 'over' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'pull'+'over'='PULLOVER'

'having' acts as a link.

Can you help me to learn more?

(Other definitions for pullover that I've seen before include "Go to side of road" , "Sweater or jumper" , "Woolly" , "Knitted garment" , "Jersey" .)

I've seen this clue in the Evening Standard.

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