Over time, all bicycles will need repairs. This is especially the case for leather seat covers. A ripped cover looks bad and can cause discomfort for the rider, which in turn can end up becoming a safety hazard. Most leather covers can be fixed with a couple of cheap materials found at any store.
Examine the seat to determine the severity of the tear. A small tear can be fixed by simply applying duct tape, but a bigger tear will likely need to be stuffed with cotton balls and then taped over.
Take cotton balls and fill the hole if necessary. Make sure the seat is still flat after inserting cotton balls.
Tape over the hole while applying pressure with your free hand as you go. This ensures a flat surface which will be comfortable to use.
If a seat is torn from end to end, you will have to have it replaced or take it into a shop and have it sewn back together.
Never ride on a damaged seat.