index.ts

const rejectOnTime = (func, time) => Promise
  .race([
    func,
    new Promise((res, rej) => {
      setTimeout(() => rej('Не успел'), time)
    })
  ])

const foo = (time) => new Promise ((res, rej) => {
    setTimeout(() => res('Успел'), time)
  })

rejectOnTime(foo(1000), 2000).then(console.log, console.log);
rejectOnTime(foo(2000), 1000).then(console.log, console.log);