In conversation, much time shared by you and me (4)

I believe the answer is:

ours

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'shared by you and me' is the definition.
(I've seen this in another clue)

I can't explain the remainder of the clue.

(Other definitions for ours that I've seen before include "Relating or belonging to us" , "What we share" , "The French bear" , "Indiscriminate slaughter" , "Belong to us both" .)

I've seen this clue in The Everyman puzzle in The Observer.

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