Welcome to the forum!
Actually, I've recently put in a feature request, to change the name of Trace Bitmap to Trace Raster Images. Because a lot of people seem to think "bitmap" means BMP. But the truth is, it will trace any kind of raster image. Just for future reference
Depending on your goal for the final result, it might work to just extend the new path so that it overlaps with the rest, so you don't see the gap. And that would certainly be easier. But there are situations where that would not be acceptable.
What you need to do is called "node editing", and this particular type of editing is a bit tricky for beginners. But I can give you somewhat of a shortcut that won't be too hard.
1 -- Drag the ends of the new path so that they overlap the trace results. They need to completely overlap, and not be just very close. Zoom in as needed, to see it better.
2 -- While it's selected, do Path menu > Stroke to Path
If you have the Node tool enabled when you do that, you'll be able to see how it changes the path. If you have the Selection tool enabled, you won't notice any difference. But it's still important to do that step.
3 -- Select both the trace results and the new path. (With the Node tool, click the trace results, hold Shift, and click on the new path.)
4 -- Path menu > Union
You'll probably notice some small changes around the area where the paths become connected. If you don't like those changes, you can use the Node tool to tweak as necessary. You can (a) drag the nodes directly. Or when a node is selected (click on a node to select it), and if it's a smooth node (meaning there's a curve rather than a corner) you'll see the node handles. You can (b) adjust those handles, to adjust the curve. Or you can (c) grab the path directly and drag the path to adjust the curve.
Dragging the path directly might be a bit tricky, since there is no stroke. But if you watch the mouse pointer, when the mouse is directly over the path, it will change from arrow to hand or fist. Then drag.
Let us know how it goes
