How to repair a cracked door frame?

Hello, my door frame is broken where the lock is located (as in the photo). I`m a complete novice and I don`t know how to solve this problem, both functionally and aesthetically, so I`m asking for suggestions.

WIKOL glue and clamps?

Ok, but how to squeeze it? And how to cover the crack with some paint or veneer?

First, I would fill the cracks with wood from the top, even slightly bending the crack so that the wood would go as deep as possible, then dry wipe the white surfaces where I expect compression, glue the left white side surface intended for compression everywhere with a 4 cm wide colorless tape, place a wider vertical board under it and place it on the glued colorless tape and on the gap, and squeezed it with two carpenter`s clamps, placed on the entire door frame together with the board, but one should be in front of the transverse gap and the other one lower, and waited at least 12 hours, and painting on the next day , after removing the colorless tape. After squeezing, wipe the front surface of any wood that comes out of the crack... The wood is white, sometimes the joint will be so white that you don`t need to paint it...

And how? It helped? I have an identical case and I don't know what to do

I would fasten it with a piece of stainless steel flat bar and screws or white screws.

I had the same experience. First, I drilled holes so that the screw head would hide. Then I poured viscosity into the crack and put 3 screws. Then I sanded the wood filler and applied the paint.