I believe he signed something saying he wouldn’t run as a third party candidate in 2016 if he lost the republican presidential primary. I don’t think Trump will run again, anyway. He can definitely champion a third party and support it.
Nobody was even thinking of 2024 at the time. Donald will run again, I think. If he doesn’t, Don Jr. seems to have acquired a taste for public speaking. I don’t approve of dynasties, but in this case it may be necessary to have another Trump go into the WH, just to right a blatant wrong, should papa be in decline or simply fed up with political back-stabbers by 2024.