It works, trust me. The problem is the assigment in:

let hours = currentTime.getHours()
let minutes = currentTime.getMinutes()
let seconds = currentTime.getSeconds()

You're assigning time once at the start, and don't check for updated values later. If you'd put that in your time function it would work properly. Something like this:

function time () {
        let currentTime = new Date()

        let hours = currentTime.getHours()
        let minutes = currentTime.getMinutes()
        let seconds = currentTime.getSeconds()

        let hoursIf = hours.toString().length==1 ? "0"+hours : hours
        let minutesIf = minutes.toString().length==1 ? "0"+ minutes : minutes
        let secondsIf = seconds.toString().length==1 ? "0" +seconds : seconds

        timer.textContent = `${hoursIf}:${minutesIf}:${secondsIf}`

}
time()
let run = setInterval(time, 1000)

You aren't updating your variables. You have them as globals, but never update their values, so the method "time" keeps using the same values.

let currentTime = new Date()

let hours = currentTime.getHours()
let minutes = currentTime.getMinutes()
let seconds = currentTime.getSeconds()

These should be set in your method or at least updated to current values. Otherwise you are simply re-displaying the same time every time executes.

If you put a "Console.log" in your method, I'd bet you'd see that it does run, it just doesn't update the time as you expect.