Clear air due to complimentary weed? (5-4)

I believe the answer is:

smoke-free

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

'clear air due' is the definition.
Both the definition and answer are adjectives. Maybe there's an association between them I don't understand?

'complimentary weed?' is the wordplay.
I cannot really understand how this works, but
'complimentary' could be 'free' (synonyms) and 'free' is located in the answer.
'weed?' could be 'smoke' (synonyms) and 'smoke' is found within the answer.
No letters remain.
This explanation may well be incorrect...

'to' is the link.

Can you help me to learn more?

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

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