Well with the right CPU you should be able to get about 56 FPS @ 1080p, so I'm guessing it is your CPU that is limiting your FPS.
Anandtech's FPS for the RX 480 4 gb GPU
Here are the requirements for The Division:
Minimum PC System Requirements:
OS: Windows 7, Windows 8.1, Windows 10 (64-bit versions only)
Processor: Intel Core i5-2400, AMD FX-6100, or better.
Memory: 6 GB RAM
Graphics: NVIDIA GeForce GTX 560 with 2 GB VRAM (current equivalent NVIDIA GeForce GTX 760), AMD Radeon HD 7770 with 2 GB VRAM, or better
DirectX: Version 11
Storage: 40 GB available space
So I don't know if the A8-7600 is equivalent to the FX 6100, but it is possible that your CPU is limiting your FPS. It's also possible that you have a temperature issue that might be throttling the CPU/GPU, so we need to know your complete specs.