Delivers suspect walk-on part? I'd stumble over scenery (10)

I believe the answer is:

extradites

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

'delivers suspect' is the definition.
'extradites' can be an answer for 'delivers' ('extradite' can be a synonym of 'deliver'). I'm not sure about the 'suspect' bit.

'walk-on part? i'd stumble over scenery' is the wordplay.
'walk-on part?' becomes 'extra' (I've seen this before).
'stumble' is an anagram indicator (I've seen 'stumbling' mean this).
'over' is a reversal indicator.
'scenery' becomes 'set' (a stage set).
'set' backwards is 'tes'.
'id' anagrammed gives 'di'.
'extra'+'di'+'tes'='EXTRADITES'

Can you help me to learn more?

I've seen this clue in The Guardian.

Want a hint initially instead of a full solution? Install my app