Currently tvOS runs at 1920x1080 but moving to 4K is a simple @2X conversion.
4K, of course, is just 1080p@2X. Easy transition, same as original Retina iPhone
Troughton-Smith notes that "the 4K transition for tvOS is going to be painless. Even upscaled images look fine, and especially on a TV screen". He also suggests that developers get started on @2x assets.
Pro tip: if you’re making art for tvOS, I’d be adding @2x elements already just to be prepared
Reports that Apple is planning to release a 4K Apple TV have ramped up lately. Back in February Bloomberg reported that Apple was testing a new fifth generation Apple TV that features 4K support and more vivid colors. The new Apple TV is allegedly codenamed "J105". Then in March, Firi Games co-founder and programmer Tijmen Roberti spotted a new mysterious "AppleTV6,2" model in Phoenix HD's logs. The device was running tvOS 11. Last month, some observant iTunes customers noticed that select movie purchases in their iTunes History were being marked '4K, HDR' and then just days ago references to a 4K HDR Apple TV with support for HDR 10 and Dolby Vision were spotted in the leaked HomePod firmware.
It appears very likely that Apple is getting ready to launch later this year. You can follow iClarified on Twitter, Facebook, Google+, or RSS for updates.