Proposed main solution with famous surrounding (9)
I believe the answer is:
nominated
'proposed' is the definition.
(nominating is a kind of proposing)
'main solution with famous surrounding' is the wordplay.
I cannot quite understand how this works, but
an anagram of 'main' is 'mina' which is located in the answer.
'famous' could be 'noted' (noted can mean well-known or famous) and 'noted' is found in the leftover letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for nominated that I've seen before include "Proposed as a candidate" , "Put forward for election" , "mentioned specifically" , "selected" .)