Remind leftist to take gentle exercise (3-4)

I believe the answer is:

jog-trot

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'take gentle exercise' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'remind leftist' is the wordplay.
'remind' becomes 'jog' (I've seen this in another clue).
'leftist' becomes 'trot' (I can't explain this - if you can you should give a lot more credence to this answer).
'jog'+'trot'='JOG-TROT'

'to' is the link.

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I've seen this clue in The Times.

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