Restoring exterior door frame at latch?
If the blue circle is accurate in your picture, there is not that much damage to keep an oversized strike from working. Home Centers carry these although they are not the best looking item, they will fix the problem easily.

Picture courtesy Home Depot

 

You may even be able to use a "tee" strike, the strike is slightly larger than the standard, easy to find in any hardware store and the holes for the screws are farther apart than the standard so you will get into new wood with the screws



Picture courtesy Lowes

If you feel you must repair the edge by adding  dutchman as it is called, I would cut out a piece centered on the damaged area out at least 8" long. Make sure the cuts are flat and accurate to aid in matching the new piece you are adding. Make sure it is fully bedded in a good wood glue. There will be drips and runs, so have a bucket of water and rag or sponge handy. Set the dutchman in place by driving in a few smal brads in the angled ends, these will act as clamps util the glue dries. If there is a way to add clamps, better still.