Terribly regally, for the most part (7)
I believe the answer is:
largely
'for the most part' is the definition.
(synonyms)
'terribly regally' is the wordplay.
'terribly' is an anagram indicator.
'regally' with letters rearranged gives 'LARGELY'.
(Other definitions for largely that I've seen before include "Allergy (anag.)" , "On the whole" , "To a great extent" , "Mainly" , "Generally" .)