Check your racket and strings
The best way to prevent tennis elbow is by having good form on your strokes, especially your backhand. Poor form often causes a player to hit the ball late or off-balance, causing their arm to have to do most of the work, rather than their torso. This can quickly cause the tendons near your elbow to become overworked. Unfortunately, if it were easy to strike the ball perfectly every time, we would all play like Roger Federer.
One thing you can do to help prevent tennis elbow is strengthen the muscles around your elbow. This will help condition the tendon and make it accustomed to enduring significant strain. Another option is changing the equipment you play with. The less vibration that reaches your elbow, the less likely the tendon will flare up. Softer strings, especially natural gut tennis strings, significantly reduce the amount of vibration that travels down the handle. Also, larger, heavier, more flexible tennis racquets with larger sweet spots will help prevent vibration from reaching the elbow.