Self-important old politician tucked into fresh soup (7)
I believe the answer is:
pompous
'self-important' is the definition.
(thesaurus)
'old politician tucked into fresh soup' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'politician' becomes 'mp'.
'tucked into' is an insertion indicator.
'fresh' indicates an anagram.
'o'+'mp'='omp'
'soup' is an anagram of 'pous'.
'omp' placed inside 'pous' is 'POMPOUS'.
(Other definitions for pompous that I've seen before include "Arrogant" , "Proud" , "Affectedly grand" , "Grandiloquent" , "Grandiose" .)