Short pause to rest in outskirts of Rugby, between Warwick and Leicester Unis? (12)

I believe the answer is:

intervarsity

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'rugby between warwick and leicester unis?' is the definition.
I can't judge whether this defines the answer.

'short pause to rest in outskirts' is the wordplay.
'short' means to remove the last letter.
'pause' becomes 'interval' (I've seen this before).
'to rest in outskirts' becomes 'rsity' (I am not sure about this - if you are sure you should believe this answer much more).
'interval' with its final letter taken away is 'interva'.
'interva'+'rsity'='INTERVARSITY'

'of' is the link.

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I've seen this clue in The Independent.

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