Processor

For Premiere, you're doing yourself a disservice by not using a discrete GPU at all, and you're using only the IGP on that CPU.

On the other hand, if you're using a really cheap discrete GPU that may actually be weaker than the IGP, then you have wasted your money on that part. So, if you really need a new GPU right away, then go with a GTX 1050 or 1050 Ti with that CPU. The GTX 1060 isn't worth it with that CPU unless you're going to also purchase the paid version of BlackMagic DaVinci Resolve.

I don't think it will help much, if at all.

You really need a faster processor before you upgrade the video card.

In addition to Neil's question, what type of video files are you editing?

MIght, although that's a slow enough CPU for speed with only 4 cores, so it's not capable of supporting a real fast one so don't waste the money on a spendy one. Maybe a GTX970 or so, inexpensive but will support that CPU.

What's the rest of the hardware and the drives connected to that computer? To get best performance with any level of gear is a balancing act of the way all the pieces work together.

Neil