First, let’s make HTML/CSS.

Each component of the time would look great in its own <span>:

<div id="clock">
  <span class="hour">hh</span>:<span class="min">mm</span>:<span class="sec">ss</span>
</div>

Also we’ll need CSS to color them.

The update function will refresh the clock, to be called by setInterval every second:

function update() {
  let clock = document.getElementById('clock');
  let date = new Date(); // (*)
  let hours = date.getHours();
  if (hours < 10) hours = '0' + hours;
  clock.children[0].innerHTML = hours;

  let minutes = date.getMinutes();
  if (minutes < 10) minutes = '0' + minutes;
  clock.children[1].innerHTML = minutes;

  let seconds = date.getSeconds();
  if (seconds < 10) seconds = '0' + seconds;
  clock.children[2].innerHTML = seconds;
}

In the line (*) we every time check the current date. The calls to setInterval are not reliable: they may happen with delays.

The clock-managing functions:

let timerId;

function clockStart() { // run the clock
  if (!timerId) { // only set a new interval if the clock is not running
    timerId = setInterval(update, 1000);
  }
  update(); // (*)
}

function clockStop() {
  clearInterval(timerId);
  timerId = null; // (**)
}

Please note that the call to update() is not only scheduled in clockStart(), but immediately run in the line (*). Otherwise the visitor would have to wait till the first execution of setInterval. And the clock would be empty till then.

Also it is important to set a new interval in clockStart() only when the clock is not running. Otherways clicking the start button several times would set multiple concurrent intervals. Even worse – we would only keep the timerID of the last interval, losing references to all others. Then we wouldn’t be able to stop the clock ever again! Note that we need to clear the timerID when the clock is stopped in the line (**), so that it can be started again by running clockStart().

Open the solution in a sandbox.