Pull ahead
Definition 1 of 2
Pro Tip 1/3Racing Context
Often used in sports or races to describe a sudden improvement in position. 
The cyclist pulled ahead in the last few meters.
Pro Tip 2/3Gradual Progress
May indicate a slow and steady process, rather than a quick surge. 
With hard work, she slowly pulled ahead of her classmates.
Pro Tip 3/3Competitive Edge
Suggests gaining a slight advantage over a competitor or challenge. 
The company pulled ahead with its innovative marketing.