Replaced Door Knobs, How to Fill Extra Space
Now that you have posted a right nice picture of the new striker plate installation let me comment on this. 


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.
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.
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.