Eminent Conservative involved in a medical upset (9)
I believe the answer is:
acclaimed
'eminent' is the definition.
(eminent means acclaimed or celebrated)
'conservative involved in a medical upset' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'involved in' indicates putting letters inside.
'upset' indicates anagramming the letters.
'a'+'medical'='amedical'
'amedical' anagrammed gives 'aclaimed'.
'c' placed inside 'aclaimed' is 'ACCLAIMED'.
(Other definitions for acclaimed that I've seen before include "Strongly praised" , "Hailed, heralded" , "Highly respected" .)