I have good news and bad news for you. The good news… any antenna should work for 4K over-the-air broadcasting, even the really old one that was on the roof when you got the house. The bad news…
There probably will never be any 4K over-the-air broadcasting. Ever.
Broadcasters aren’t required to put out a 4K signal and that means that they probably won’t. The only reason you see HD today is because a move to digital broadcasting was mandated by the FCC back in the 2000s and while that didn’t technically require a move to HD, it did make sense to put in HD equipment in most stations when they were switching over to digital.
There is actually a broadcast standard for 4K that would allow broadcasters to put out a 4K signal using the same 6MHz channel that they currently use for broadcasting HD. There’s some question as to whether the quality would be any good, but there’s nothing technical that would prevent them. The ATSC, the group that designed today’s TV standards for North America, has created the ATSC 3.0 standard which includes 4K. Unfortunately the standard hasn’t been approved or even considered for US broadcasting as of yet, and it likely won’t be.
Transitioning from analog to digital was a pretty massive undertaking, the sort of thing that comes about once in a generation or so. It’s not likely that already cash-strapped broadcasters are going to pitch all their HD equipment to move to 4K so quickly. This is especially true when you consider that there just isn’t a demand for 4K content like there was for HD content, and when you further consider that most people consider the future of television to rely just as much on streaming as it does on broadcasting.
Getting back to the question at hand, though, since there is a technical standard for putting 4K on the same channels as HD, and since there is plenty of channel space out there in the UHF and VHF bands (too much in fact, since the FCC is considering taking spectrum away from broadcasters to give it to mobile users) there is no reason to think you’d need a different antenna. After all, an antenna doesn’t know and doesn’t care what kind of signal it receives as long as it’s within the frequency range that it’s designed for. So bring on the 4K, your antenna can take it… but don’t hold your breath waiting for it.