This is a hand rest for bass trombone and contrabass trombone made by Kuhnl & Hoyer in Germany. While designed for K&H instruments, it may fit some others. The clamp fits 10mm-11mm diameter braces (0.394"-0.433") with the included 0.5mm shims.
The second photo shows the hand rest properly installed on a K&H bass trombone - plenty of room for your hand.
The third and fourth photos show the K&H hand rest installed on a Getzen 3047AF tenor trombone because a client inquired whether this would work. It doesn't really fit that tenor very well. The bell section and main brace are too narrow, plus the modular bell screw is in the way, making the brace too close to my hand. You could bend the brace rod a little, but for that situation, there is probably another brand to look for.
We have other hand rests made by Edwards and Neotech.