Factory I support in an instant (11)

I believe the answer is:

millisecond

'an instant' is the definition.
(thesaurus)

'factory i support' is the wordplay.
'factory' becomes 'mill' ('mill' can be a synonym of 'factory').
'support' becomes 'second' (I've seen this before**).
'mill'+'i'+'second'='MILLISECOND'

'in' is the link.

(Another definition for millisecond that I've seen is " extremely short period of time".)

I've seen this clue in The Times.

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