You need to define a global variable and check if it is true , not to fire the first function. But there may be some runtime problems , if between running the first event , second event called , first event will not freeze and continues to run.

let shouldRun = true;
obj.addEventListener('suspend', () => {
  // when only this is fired -> run this code

if(!shouldRun){
  return;
}
// my code
});

obj.addEventListener('play', () => {
  // when this is fired too -> run this code and deactivate the first code
  shouldRun = false;
  // my code
});

I guess You can try using obj.removeEventListener('suspend') on the Call of 'play' event.

For more about removeEventListener, you can go through the official link. https://developer.mozilla.org/en-US/docs/Web/API/EventTarget/removeEventListener

A simple way to solve this is to remove the event handler with removeEventListener().

function handleSuspend() {
  // when only this is fired -> run this code
  
  // my code
}

function handlePlay() {
  // when this is fired too -> run this code and deactivate the first code
  obj.removeEventListener('suspend', handleSuspend);
  
  // my code
}

obj.addEventListener('suspend', handleSuspend);
obj.addEventListener('play', handlePlay);