Left a PS: The dog does it (4)

I believe the answer is:

laps

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'dog does it' is the definition.
I can't tell whether this defines the answer.

'left a ps' is the wordplay.
'left' becomes 'l' (common abbreviation).
'l'+'a'+'ps'='LAPS'

'the' is the link.

Can you help me to learn more?

(Other definitions for laps that I've seen before include "Circuits of a racetrack" , "Scoops up with the tongue" , "Circuits of track" , "Pals doing rounds of the track" , "Drinks; circuits" .)

I've seen this clue in the Sydney Morning Herald.

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