js - How to call an async function within a Promise .then()

Your approach using await in an async then callback will work, but it's unnecessarily complex if all you want to do is call the async function and have its result propagate through the chain. But if you are doing other things and want the syntax benefit of async functions, that's fine. I'll come back to that in a moment.

async functions returns promises, so you just return the result of calling your function:

function functionThatCannotHaveAsyncKeyword() {
    functionA()
        .then(function() {
            return functionB(someArgument);
        })
        .then(function() {
            console.log('last');
        }); // <=== Note: You need a `catch` here, or this function needs
            // to return the promise chain to its caller so its caller can
            // handle errors
}

If you want to pass functionA's resolution value into functionB, you can do it even more directly:

functionA()
    .then(functionB)
    // ...

When you return a promise from a then callback, the promise created by the call to then is resolved to the promise you return: it will wait for that other promise to settle, then settle the same way.

Example:

const wait = (duration, ...args) => new Promise(resolve => {
    setTimeout(resolve, duration, ...args);
});

async function functionA() {
    await wait(500);
    return 42;
}

async function functionB() {
    await wait(200);
    return "answer";
}

functionB()
.then(result => {
    console.log(result); // "answer"
    return functionA();
})
.then(result => {
    console.log(result); // 42
})
.catch(error => {
    // ...handle error...
});

Coming back to your approach using an async then callback: That works too, and makes sense when you're doing more stuff:

const wait = (duration, ...args) => new Promise(resolve => {
   setTimeout(resolve, duration, ...args);
});

async function functionA() {
    await wait(500);
    return 42;
}

async function functionB() {
    await wait(200);
    return "answer";
}

functionB()
.then(async (result) => {
    console.log(result); // "answer"
    const v = await functionA();
    if (v < 60) {
        console.log("Waiting 400ms...");
        await wait(400);
        console.log("Done waiting");
    }
    console.log(v);      // 42
})
.catch(error => {
    // ...handle error...
});

You can use promise inside the first method as

function functionThatCannotHaveAsyncKeyword() {
    return new Promise(async(resolve, reject)=> {
          await functionA();
          await functionB();
          console.log('last');
          resolve();    
      });
  }

  async function functionA() {
      console.log('first');
      await someServiceThatMakesHTTPCall();
  }

  async function functionB() {
      console.log('second');
      await someServiceThatMakesHTTPCall();
  }