Yes, a 4K Roku, either Streaming Stick or other models, will work fine with an HD set. My Streaming Stick+ is in use on a 720p JVC set and my Streaming Stick 4K+ is in use on a 1080p Samsung TV. Both are 4K sticks and both work fine.
The Roku communicates with the TV when the HDMI connection first starts up in what is called a "handshake". The TV tells the Roku what resolutions it supports and the Roku uses that information to set its communication protocols with the TV. I've never had a problem with this, but just to be sure, after initial setup I manually set the Roku's "Display type" setting to the connected TV's actual resolution rather than relying on the "Auto detect" setting.
Roku Community Streaming Expert
I am not a Roku employee, only a user like you. Please, no support questions via private message -- post them publicly to the Community where others may benefit as well.
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Streaming Stick 4K+ 3821 | Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X
