Accompany new score with time (6)
I believe the answer is:
escort
'accompany' is the definition.
(I know that escort is a more specific form of the action accompany)
'new score with time' is the wordplay.
'new' indicates anagramming the letters.
'with' is a charade indicator (letters next to each other).
'time' becomes 't' (abbreviation).
'score' anagrammed gives 'escor'.
'escor'+'t'='ESCORT'
(Other definitions for escort that I've seen before include "restraint" , "Person accompanying another" , "conduct" , "Companion, perhaps for protection" , "going in convoy" .)