External Graphics Card/eGPU or new laptop?

Simple. You need to buy a new laptop to run any newer version of Premiere Pro at all. You see, your laptop has too weak (read: substandard-performance) of a CPU and no discrete GPU whatsoever (in addition to the insufficient amount of installed RAM). On top of that, since CC 2015, Premiere Pro now officially requires 8 GB or more RAM.

I use a laptop with an eGPU. The eGPU helps, but only in areas that are bottlenecked by the relatively weak graphics hardware in the laptop. If the problem with your laptop is that it has only 4GB RAM, an eGPU won’t solve that, because RAM requirements are a separate issue from graphics hardware and VRAM requirements. Video editing is one of those disciplines that requires a balanced computer, where all of the necessary components — CPU speed/cores, RAM, graphics/VRAM, cooling, storage speed/capacity — need to perform at the level required by the software. If any one of them is not at the required level, like having only 4GB RAM, that one weak link can bottleneck the performance of the entire system. That’s why an eGPU won’t help enough.

If you need to have something portable, then get a current laptop that has properly balanced performance across all of the components listed above.

If it doesn’t need to be portable, definitely get a desktop computer instead. One with good cooling and easy replacement of components.

This includes "some" laptop discussion

This includes 2 recommendation links from Puget Systems... copied from Peru Bob
https://community.adobe.com/t5/video-hardware/premiere-pro-hardware-articles-to-read-before-you-buy-or-build/m-p/11557686

Moved to the Video Hardware forum.

If you can, get a desktop, you still have that computer to take with you. But otherwise, yes, you'll need a new computer. Desktops are far more powerful.