I have set up a trigger in tag manager. See below. It is my intention to log all outbound links. When i then log into my google analytic account i can't locate this data. Where would it be display. Also how long does it take for this data to be displayed.
Triggers are internal to GTM only and cannot be seen in GA. Depending on the type of tag you have created that is fired by the trigger, you may or may not be able to see tag in your GA reports as well (eg. Custom HTML, depending on how it is configured).
An event tag for outbound link clicks should show up on your Behavior > Top Events report in GA, but not the trigger itself. You may need to wait up to 24 hours for events to show up in your reports, but if your tags are working then you should be able to see them in your real time reports right away.
Edit: To track outbound clicks, you need to create your Google Analytics Event tag, with the appropriate category, action, and label, and then for your trigger, just use the one you have created already. These two together (tag + trigger) will create the outbound click event that would be recorded into GA.