I am not using that but if you look at my Premiere Pro BenchMark (PPBM) you can see that among the test results suibmitted to me that it ranks second to last in CPU performance
Are you using GPU accelerated features and effects? Only then will a newer GPU help you, but it will not make up for a weak CPU.
According to that list of CPUs Bill listed in the PPBM8 site, even the massively power-hungry FX 9590 (the highest that any AM3+ CPU ever went) is as slow as or slower than a recent, quad-core, non-hyperthreadable Intel Skylake or Kaby Lake i5 CPU in the software-only MPEG2 DVD encoding test. As such, AM3+ is at a complete dead end, and any meaningful hardware upgrades to that CPU platform will become almost totally wasted.
And because that FX 8350 is so weak, even your current GTX 970 is a bit overkill for your system. However, since there are currently no viable newer-generation GPUs that are slightly slower than either the GTX 970 or 1060 without a significant downgrade in performance, I would suggest that you stay put until you earned enough money to purchase an entire new system build instead of wasting a single penny on that weakling platform for a component upgrade that might not deliver a worthwhile enough performance increase to justify the added monetary cost.