Your sentence is almost correct, but it can be made clearer with a small change.
Original sentence: Urials wear their horns with pride. The bigger the horns, the more respect you get in the herd.
Corrected sentence: Urials wear their horns with pride. The bigger their horns, the more respect they get in the herd.
Explanation: We use 'their horns' because the horns belong to the urials. Then, instead of 'you get', we say 'they get' because we're talking about the urials, not 'you'.
So, this sentence tells us that urials are proud of their horns, and the bigger the horns they have, the more the other urials respect them in the group called a herd.