A tear in car upholstery is not always easy to repair, but with time and patience, most people can repair small holes without having to pay for expensive materials and tools. You can take your car to an upholsterer to be repaired, but they tend to be expensive and often end up recovering the whole seat. Frequently they cannot match the original fabric, so you end up with seats that do not match and a big bill.
It is easier to repair fabric seats, than vinyl seats. All you need is a strong needle and good thread, both of which you can buy from your local arts and craft shop. Match the colour of the thread to your car seat carefully a good match is key to getting a reasonable result. Make sure that the needle you buy can cope with thick fabric, but has a small enough eye to pass through the fabric without leaving holes. Check that the thread can pass through the eye too. Upholstery thread is thicker than sewing thread.
Do not to be tempted to stitch the tear together as you would a tear in an item of clothing. If you stitch the tear like this, it will be too tight and another tear will appear alongside the original tear. The seat fabric must still be able to give a bit when someone sits on the seat.
Create a grid of stitches along the length of the tear. Those initial stitches are not designed to pull the tear together in any way; they are there to add strength and structure. Now you are ready to put in the stitches that will repair the tear, along its length. Do this as you would for any normal tear but do not tighten the stitches as much as you would normally. The repaired fabric needs to have some give built into it.
The stitching you have made needs to be protected from the friction that occurs when people sit in the repaired chair. A layer of fabric gel should provide adequate protection; periodically renew this protective covering.