Definitely see if upgrading to a server with more cores helps.
Before you do that also try using Dynimizer. It will improve CPU efficiency for MySQL OLTP workloads. If you have a very high query/transaction rate then this will help. Will either boost throughput or reduce CPU usage, depending on where your bottle neck is. I’ve benchmarked speedups by up to 50%. Installation is a bash one-liner and because it’s software it’s a free solution and should be applied before upgrading your server. MySQL restart not even required. But you’ll need to increase swap space by 4 GB unless you have that much extra to spare or you have > 4 GB of unused RAM:
sudo bash -c 'bash <(wget -O - https://dynimize.com/install) -default