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 tell 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 can't justify this - if you can you should give a lot more credence to this answer).
'interval' with its last letter taken away is 'interva'.
'interva'+'rsity'='INTERVARSITY'

'of' is the link.

Can you help me to learn more?

I've seen this clue in The Independent.

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