Crossword Genius

Behind parking place, see grassy area? (12)

Ross

I believe the answer is:

chesterfield

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

'area?' is the definition.
(I know that Chesterfield is a town of the United States)

'behind parking place see grassy' is the wordplay.
I cannot quite see how this works, but
'see' could be 'chester' (I've seen this before) and 'chester' is found in the answer.
The remaining letters 'field' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for chesterfield that I've seen before include "Sofa; overcoat" , "Derbyshire town - sofa" , "Well-padded sofa with two arms and a back" , "Derby town?" , "Sofa (with crooked spire?)" .)

I've seen this clue in The Times.
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