Umpire to falsify extended time given new time in cooler (11)

I believe the answer is:

refrigerant

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'cooler' is the definition.

'umpire to falsify extended time given new time' is the wordplay.
'umpire' becomes 'ref' (short for referee).
'to falsify' becomes 'rig'.
'extended time' becomes 'era' (long period of time).
'given' says to put letters next to each other.
'new time' becomes 'nt' (this could be a standard abbreviation of which I'm unaware).
'ref'+'rig'+'era'+'nt'='REFRIGERANT'

'in' is the link.

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I've seen this clue in The Times.

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