Run away fast, for the most part (4)
I believe the answer is:
flee
'run away' is the definition.
(thesaurus)
'fast for the most part' is the wordplay.
'fast' becomes 'fleet' ('fleet' can be similar in meaning to 'fast').
'for the most part' means to remove the last letter.
'fleet' with its last letter taken away is 'FLEE'.
(Other definitions for flee that I've seen before include "head for the hills" , "Leave" , "Run quickly away" , "Take flight" , "Maybe escape" .)