Lag back; ran with easy strides as a quadruped (8)

I believe the answer is:

galloped

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'easy strides as a quadruped' is the definition.
I can't judge whether this defines the answer.

'lag back ran' is the wordplay.
'back' is a reversal indicator.
'ran' becomes 'loped' (loping is a kind of running).
'lag' backwards is 'gal'.
'gal'+'loped'='GALLOPED'

'with' is the link.

Can you help me to learn more?

(Other definitions for galloped that I've seen before include "'I - - , Dirck - - ...' (Browning)" , "Went quickly by horse" , "Ran" , "Rode fast" , "Went at a very fast gait" .)

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

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