Don't proceed with flower in supermarket (8)

'supermarket' is the definition.

'don't proceed with flower' is the wordplay.
I cannot quite understand how this works, but
'with' could be 'w' (abbreviation) and 'w' is present in the answer.
'flower' could be 'rose' (I've seen this before) and 'rose' is present in the answer.
The remaining letters 'ait' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'in' is the link.

Can you help me to learn more?