Since our jerseys are knits - made with a series of loops instead of woven. The Best thing to do is to take a needle and thread and sew the rough bits together - try to rejoin the loops. It won't look like brand new. Of course you could patch it.

Best and most creative repair I did was on a colleague's shark jersey after he crashed. Some of the jersey was actually missing, so there were no edges to be brought back together. After he washed it, (I don't work on dirty clothes), I used some red jersey fabric for the holes, sewn down with a zigzag stitch on my sewing machine. Then used fabric paint to add some more "blood" to the water and dripping off the shark's teeth. Just so happened that the hole was in the middle of the jersey's circling shark's, so the design wasn't lost too much.

One thought about the patches - the back of the patches can be scratchy, so you don't want that next to your skin. You'll need to pull together as much of the jersey tear and sew that before you add the patch. Also, the patches I'm guessing are woven, which means they won't stretch as if they were jersey, which will alter the fit of your sleeve.