Repairing small tears in your outdoor gear is a fact of life. Some folks like the old standby, duct tape, but the results are usually Less Than Ideal - an unsightly panel of grey tape on your gaiter, pack or jacket, peeling glue, and a short life span.
A better alternative is to use seam grip, an adhesive available in most any outdoor store. (Lacking this, most general purpose household clear adhesives work as well.)
To fix a tear, put some tape (most any kind will do) on the outside of the gear you are fixing - in this case, a gaiter. Next, turn the gaiter so the inside is facing toward you, and reposition the flapping piece by pressing it down on the tape so it’s temporarily held in place. Now, put a good layer of adhesive on the tear, let it cure overnight, and then remove the tape. You’ll have a fix that’s durable, almost invisible, and fast.
For a more substantial year in a thin fabric that's going to have some tension on it, such as a tent fly, try putting down a layer of seam grip, then lay in a layer of cut mosquito netting, and then put some more seam grip on top of that. Read more on this technique at this tip.