Extreme public storm somehow overshadows race's conclusion (9)
I believe the answer is:
outermost
'extreme' is the definition.
(thesaurus)
'public storm somehow overshadows race's conclusion' is the wordplay.
'public' becomes 'out' (out can mean released to the public).
'somehow' indicates anagramming the letters.
'overshadows' is an insertion indicator (the inserted letter is smothered or overshadowed).
'conclusion' indicates one should take the final letters.
The final letter of 'race' is 'e'.
'storm' is an anagram of 'rmost'.
'rmost' placed around 'e' is 'ermost'.
'out'+'ermost'='OUTERMOST'
(Another definition for outermost that I've seen is " farthest from centre".)