Cinder circuit to follow after woman, right? (4-5)

I believe the answer is:

dirt-track

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'cinder circuit' is the definition.
'dirt track' can be an answer for 'circuit' (dirt track is a kind of circuit). I'm not certain of the 'cinder' bit.

'follow after woman right?' is the wordplay.
'follow' becomes 'track' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'woman' becomes 'di' (short for Diana).
'right?' becomes 'rt' (abbreviation as in Rt Hon- the Right Honourable).
'di'+'rt'='dirt'
'track' put after 'dirt' is 'DIRT-TRACK'.

'to' acts as a link.

Can you help me to learn more?

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

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