First you need to expand the trace to make it editable. Then with the direct selection to you can select the end points of two line and then join them.
That said, that could make or break what you are doing, it depends if the path is the outside or the inside. I should say it this way, it depends if the path is the object or the hole in the center. You may be connecting to the wrong line if you can not determine which path is which.
Just something to keep in the back of your mind, if it doesn't work as it should.