If your simply looking to add links, there are some theme components that already accomplish this, such as:
Looking at the code these may give you a hint into accomplishing what you’re looking for, but in short, you would need to leverage Discourse’s pluginAPI to decorate an existing widget in the header, such as header-buttons:before and then you can use the virtual-dom to add anchor tags. Take a look at this guide for more information on that.