I assume your streaming device is wireless - a router just splits a single external ip into an internal local ip range - so adding another one will do nothing for speed.
Assuming that the initial connection you have that comes into the house is adequate - the issue is one of the following:
The speed the router has (if it is an old one, might be time to replace it)
The strength of the signal where you want to consume it (options are upgrading the router to a modern one or adding coverage)
The speed of the consumer (If this is an old Roku box, it might not have up to date wifi support).
So, adding another router is not going to do anything. You either replace, enhance it to provide access if the signal where you want to consume is bad or upgrade the consumer.
FWIW - We have multiple brick walls in the house - brick really hurts transmission speed and strength. The solution for us was to upgrade our router into a modern Mesh router (went with an Eero one, but they are all good) - and it solved the problem. Because I also wanted service in the garage which is a separate building, I also installed a beacon in the house at the closest place to the garage (a beacon for a mesh system is like a repeater for old Wifi systems but without speed loss) - and it allowed us to get service there as well.
So, If you want some more concrete advice - tell us what you have now - maybe it will be obvious where the bottleneck is.