Here are a few tips on how to get faster. Run stairs, but change up how many stairs to skip and don't just jog up the stairs, run as fast as you can. When you hit every single step you really work on your foot speed and skipping steps works on your leg power.
Next, do wind sprints where you start at a walk and work into a full sprint. You can do these on a track.
Finally, starts are a great way to get your speed up. From a sprinters start, sprint full speed for 30 meters, walk back to the start, get into position and repeat for 6 starts.
Doing starts and stairs inbetween cross-country and track immensely improved my sprint speed as I was a middle
distance runner in track and on the 4x200.