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Walk briskly, then run from Tea Party participant (5,4)

Ross

I believe the answer is:

march hare

I'm a little stuck... Click here to teach me more about this clue!

'tea party participant' is the definition.
I can't tell whether this defines the answer.

'walk briskly then run' is the wordplay.
'walk briskly' becomes 'march' (marching is a kind of walking. I am not sure about the 'briskly' bit.).
'then' means one lot of letters go next to another.
'run' becomes 'hare' (hare can mean to run very fast).
'march'+'hare'='MARCH HARE'

'from' is the link.

Can you help me to learn more?

(Other definitions for march hare that I've seen before include "seen at endless party" , "One in Tea Party" , "Character at the tea-party in Alice's Adventures in Wonderland" , "Animal in state of wild behaviour, starting with 3rd month?" , "Ditto" .)

I've seen this clue in The Independent.
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