Replaced Door Knobs, How to Fill Extra Space

Most locksets are adjustable from about 1 3/8" up to 1 3/4" thick doors. (See screw mechanism in center of unit.) If yours is not or door is less than 1 3/8" thick, the piece of door hardware you're looking for is called a "door rose". It fits between the knob and the door and comes in various shapes, thicknesses and finishes. Google: rose hardware door with lock

If you can't find it on your own, try Emtek.com. Very reputable, but bad website. I can't ever find a thing. Call them...excellent service.

Now that you have posted a right nice picture of the new striker plate installation let me comment on this.

1. The craftsman way to fix this is to cut out a section of the door frame where the old striker plate and its recess holes are located (plus some extra). Then a carefully cut and fitted new piece of wood is glued into place to make the door frame whole again.
2. The new striker plate would be installed over the new wood region with the appropriate blind depth recess holes made behind it to permit the door catch and deadbolt enter the frame area beyond the striker plate.
3. Note that it is not conventional practice to mount the striker plate on top of the surface of the door frame as you showed in the picture. The normal process is that the outline of the plate is marked and then some wood chisel work is done to recess the plate by an amount equal to its thickness so that its surface is even with the door frame surface.

You can fill that void between the strike plate and door stop with Durhams Rock Hard Putty. It's a powder that you mix with water. Fill that area so the putty is higher than the jamb surface and you will be able to sand it down to smooth when dry. A bit of primer over the putty and you'll be ready for paint.

So add wood putty because you can always chip out when you have needs to adjust striker due to inevitable heat/cool expansion/ contraction.