You're looking for event tracking. You can bind an event tracking call to absolutely any interaction with a webpage (or non-interaction such as firing an event after a predefined period of time - remember to set the 'non-interaction' flag!).
The basic code for event tracking is as such:
ga('send', 'event', '[category]', '[action]', '[label]', [value]);
So if you have a HTML anchor element (hyperlink) you will want to bind this to the onclick event. I'll demostrate this by hardcoding it, but you could dynamically bind using native JS or something like jQuery of course:
<a href="http://www.shinyhappypeople.com" onclick="ga('send', 'event', 'User Interaction', 'link-click', 'shinyhappypeople.com', 1);">click me</a>
For full details of everything you can do with event tracking just see the Google Docs here.