pull ahead
phrasal verbwithpullverb[T]uk/pʊl/us
tostartto do well or to dobetterthan someoneelse:
It wasslowat first, but we'restartingtopullahead.
pull ahead of sb/sthAfter adisappointingyear, thecompanyisfinallypullingaheadof thecompetitiononcemore.