What games are you playing and what are your full specs? For games like CSGO, your current CPU+GPU will do 140+ FPS at 1080p medium settings, however 140fps isn't possible with your setup in modern AAA titles running at higher settings.
A GTX 970 is only going to do 140fps at 1080p lower settings or lower resolutions (720p likely) in modern titles, but if your fine with lower settings, your GPU can stay since it is currently held back by your CPU in a lot of tasks. The 7-year-old 4c/8t Xeon with mid 2ghz clocks certainly can't handle modern high refresh gaming, so an upgrade is necessary.
You may need a platform upgrade to get 140+ fps in modern titles since that platform is quite old and even high-end CPUs for your existing motherboard likely aren't capable of 140fps in modern games. 16gb of ram is an adequate amount for the task, however, DDR3 is not supported by modern platforms.
I would suggest an upgrade to a modern AMD Ryzen 7 or Intel Core I7 CPU (maybe R5 or I5 if $ tight) and upgrading GPU later, depending on games you play and budget. A new mobo and ram are needed for this upgrade.
Well, the CPU here is probably a massive bottleneck, and you would definitely be able to get 140+ FPS in some games with an upgrade of the CPU, even the best CPUs for the socket on your motherboard are not enough to play newer games. You'll want a new motherboard, a new CPU to go with it, and some DDR4 memory in order to use the 970 to its full potential.
Expect to pay somewhere around $400-500 for a platform upgrade capable of 140fps+ excluding a new GPU. Running modern games at high refresh rates takes a lot of CPU horsepower, which is not cheap. Expect to pay even more for an Intel route. If you are fine with 60 fps or even 100 fps you could go with a fair bit cheaper setup. 60fps should be capable with your setup.
Example setup: PCPartPicker part list / Price breakdown by merchant