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Here's a Typescript version of @Heniker's answer with perhaps better naming.

function pushToExecQueue<T>(fn: (...args: any[]) => Promise<T>): (...args: any[]) => Promise<T> {
  let inprogressPromise = <Promise<T>>Promise.resolve();
  return (...args) => {
    inprogressPromise = inprogressPromise.then(() => fn(...args));
    return inprogressPromise;
  }
}

And perhaps a somewhat cleaner/clearer way of using it is

pushToExecQueue(myAsyncFunction)("Hi", "my second parameter", etc);

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