Popular king to relieve inflation (8)
I believe the answer is:
increase
'inflation' is the definition.
(thesaurus)
'popular king to relieve' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'king' becomes 'CR' (short for Carolus Rex, King Charles in Latin).
'to relieve' becomes 'ease' (easing is a kind of relieving).
'in'+'cr'+'ease'='INCREASE'
(Other definitions for increase that I've seen before include "rise in wages, perhaps" , "Multiply" , "Wax" , "Become bigger or greater in amount" , "Amplification" .)