I'd add framing, so you can attach the hardware cloth to it, along with your existing fence. We used fencing staples, and then covered each seam with 1"x4" boards, screwed to the framing, which is mostly 4"x6" posts.
Thinking ahead about those raccoons reaching in, and two 100 lb. dogs tearing at it. For bears, electric is the only thing...
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In winter we use two layers of rolled plastic (vinyl) on the lower 6' as a windbreak.
View attachment 1898464 View attachment 1898465 All old pictures, but hope it helps, Mary