Crossword Genius

Continue with cliffs just after cutting south (5,2)

Ross

I believe the answer is:

carry on

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'continue' is the definition.
(carry on can mean to continue or keep going)

'cliffs just after cutting south' is the wordplay.
I cannot quite understand how this works, but
'just after' could be 'on' and 'on' is present in the answer.
The remaining letters 'carry' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

'with' is the link.

Can you help me to learn more?

(Other definitions for carry on that I've seen before include "Continue like English series of risque films" , "Don't stop" , "Keep going!" , "in-flight baggage" , "Continue - to-do" .)

I've seen this clue in The Telegraph.
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