Did you convert it into a Morph?
Because if you did, then all you need to do is either directly select that edge ( Control+Shift on Windows, until the cursor arrow turns white from black) and then pull it or move it wherever you want via the pet palette move button (#2 in the image below).
Alternatively rather than actively moving it and depending on the rest of the geometry, you can directly Extrude it using the extrude edge option on the pet palette (#1 on the image below).
But with this option you have to be aware that it will only extrude perpendicularly as constrained from the adjacent or connection edges or vertices - meaning, you may not be able to extrude it how you want in a direction you want.
You might want to test both methods and see which works for you.