I am NOT a Sprint Coach.
However, some aspects that can be looked at are:
1. Sprinting is ENTIRELY different from Long Distance Running. You’ll therefore, need to get stronger as this will definitely develop your muscles to aid you in increasing your sprint speeds.
2. Strength Exercises such as the Squat, the Deadlift, the (Overhead) Press, the Benchpress and Chinups should help you get Stronger.
3. Do NOT look at this separately as those Exercises that Develop specific parts of the body. You need to look for Compound Exercises (mentioned above), that work your Entire Body.
4. As obvious as this sounds, you need to discuss with a Qualified Sprint Coach to work out a proper Sprint Training Program, that will help you Increase your Sprinting Speeds, and will need to diligently follow the program, while Continually working with your Spring Coach. There is no one (or two or three) magic things that will get this done.
5. Ideally, you want to also approach a QUALIFIED STRENGTH & CONDITIONING Coach, to design an S&C Program and then, to stick with the program, in communication with your S&C Coach.
6. Again Ideally, you also want to involve a Sports Nutritionist, to ensure that you get the proper Nutrition…that will help you gain Strength, while at the same time, help you minimize (gaining) Extra Body Fat.
From a General Perspective, you will therefore need to
a. Get Stronger
b. Improve Technique so you use your body more effectively
c. Get more Aerodynamic
d. Use Proper Equipment while Training and in Competitions
e. Ensure you get Adequate Rest & Recovery
f. Take care of your Nutritional Requirements
All the above, should help you gain Sprint Speed (in fact, will help you get good/better in any Sports).
Hope this helps!