Installing a new exterior door into a taller existing opening
The simple answer is to fix a 4" high piece to the top of the frame where the door would go.

However, you would need this to match the thickness of the new door you are fitting and you'd need to weatherproof the gap between this and the new door. Assuming that the door opens inwards you could fit a piece of wood across the gap.



Paint the wood the same colour as the frame to de-emphasise it, or paint it a contrasting colour (the same as the door perhaps) to highlight it.