Lets say I have something like this:
How could I create an edge loop around the model that includes the circled edge?
Blender Stack Exchange is a question and answer site for people who use Blender to create 3D graphics, animations, or games. It only takes a minute to sign up.Sign up to join this community
That wouldn't be an edge loop, also by doing so you create triangular faces. To do that, you make an edge loop cut like you usually do. And then you merge vertices of your unwanted edge to the existing edge. By properly selecting "merge to last" or "merge to first", your existing edge will stay where it was.