https://i.imgur.com/dZ3h5Bl.jpg

If it's a removable cover: put a bit more than a dab of fabric glue on a small square of fabric (say 4x the size of the hole) and glue said fabric square to the under/back side of the hole.

While glue is damp, get a needle and straighten the fibres out to sort of stretch/cover the hole.

If not a removable cover move the fibres around then put less fabric glue, applied with needle so it's very fine, just where broken fibres are.

Lots of quick vids on YouTube.

You could do a sewing technique called darning. There are pretty cool videos on different ways to do it.

Sewing?

Sew it with a curved needle and matching thread. First knot can be hidden by going in the hole and up by the edge, final knot you bury by going in the end of the hole, come up about a half inch away (any direction) and cut the thread flush with the fabric, end of the thread will just disappear.

Glue will feel crusty and be much more obvious

I’d recommend darning. Get a white thread and zig zag across the hole using really small stitches with low tension, and that should be nearly invisible. See link for a really cruddy diagram! cruddy diagram

The difference between this and just sewing it up is that the stitches lay flat, rather than having a raised bump like you would with a whip stitch, and the edges are covered to prevent fraying. By weaving over and under, including at both ends, the tension from the stitches is distributed over a larger space, so it doesn’t just tear where you put the stitches in later.

Great advice! I think I'll give this method a try!