You would have a clock with a second hand 2.86 million km long. Well, a little shorter, as the end can't actually move at lightspeed
In practical terms, you're going to have difficulty driving the thing. There's no material rigid enough that it could be spun up to such a speed by rotation of the central axle, and no material strong enough not to snap and fly apart.
The time being displayed would be unaffected by relativistic effects. Don't get hung up on the fact that this is a timepiece; in physics terms, it's just a rotating rod. The tip will be experiencing relativistic effects, but not anybody far enough away to read the time.