Lady's way about debate that's most urbane (9)

'most urbane' is the definition.
Both the definition and answer are superlative adjectives. Maybe there's an association between them I don't understand?

'lady's way about debate' is the wordplay.
I cannot quite see how this works, but
'way' could be 'st' (abbreviation for street) and 'st' is found in the answer.
'debate' could be 'moot' (synonyms) and 'moot' is found within the answer.
'lady' could be 'she' ('she' refers to a woman) and 'she' is found in the leftover letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

'that's' acts as a link.

Can you help me to learn more?