Stay in touch with the leaders (4,2)

I believe the answer is:

keep up

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'stay' is the definition.
(thesaurus)

I can't explain the remainder of the clue.

(Other definitions for keep up that I've seen before include "Progress at same pace as others, or maintain appearance" , "Match pace or store aloft" , "' - - with the Joneses'" , "Stay with the pace, don't fall behind" , "Don't dawdle!" .)

I've seen this clue in The Globe and Mail.

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