Established Latin trio somehow inspires commercial (11)
I believe the answer is:
traditional
'established' is the definition.
(thesaurus)
'latin trio somehow inspires commercial' is the wordplay.
'somehow' indicates an anagram.
'inspires' means one lot of letters goes inside another (inspire means to breathe in).
'commercial' becomes 'ad' (abbreviation for advertisement).
'latin'+'trio'='latintrio'
'latintrio' anagrammed gives 'tritional'.
'tritional' enclosing 'ad' is 'TRADITIONAL'.
(Other definitions for traditional that I've seen before include "Type of jazz" , "Following earlier usage" , "Old-fashioned" , "Following accepted usage" , "Following established custom" .)