Need for Speed Hot Pursuit Remastered

I believe the first event you can use an EMP in is 'Denial of Service', a Highway Patrol event. This is also available in multiplayer immediately.

To use these, wait for it to charge up and get behind a target. Press left on the D-pad to activate the EMP. You'll need to stay behind them for the duration of the countdown. Once it does, their car will freak out and you'll have fulfilled the requirement.

Note that this can be obstructed by certain things. You can't crash out (and neither can they, or you won't get a hit, though if you're desperate you are allowed to turn around). A Jammer will ruin your attempt and the only thing to do is wait for it to expire and try again.