Generic distro kernel? You shouldn’t have any problems.
Hand-compiled kernel cooked up with -march=native? You’re sticking with AMD, so there should still be no issues unless some instruction got dropped between the old CPU and the new, which almost never happens. You might have to add a kernel module or two for things built into your mobo, nothing serious.
(Hell, I had a Windows 2000 install on a multi-boot system survive an upgrade like that, once upon a time. Just booted perfectly happily on the new hardware.)