Please bear in mind that this is not a full-on tutorial. I have included an order of construction but I didn't take any pictures of the sewing. It's not really a difficult thing to make but it includes some tricky bits. Not for beginners, I would say
All the pattern pieces in these pictures are without seam allowance. It's important to remember that.
As mentioned, the skirt has no side seams, that seemed with nicest option because it was clear from the picture that those pockets curved around the wearer's side. So, you start by placing the front and back of your skirt block with their sides together. And because this skirt closes with buttons down the front, add 2 cm along center front.
Then, you draw in the design. I've used red for the alterations on the skirt itself and blue for the other pieces.
I took 1.5 cm from the back dart at converted that to shaping of the center back seam. I knew from my recent re-drafting of my skirt sloper that this suits my figure really well, you don't have to do this. If you don't, simply follow the next steps using the full back dart. If your sloper has two back darts (and you really need them because the combined width is more than 5 cm) I would recommend keeping one in the back skirt.
Draw in the top of the pocket. Mine is 5 cm below the waistline, starts at the front dart position and extends into the back for a bit less of that width. The pocket edges follow the angle of the darts.
Draw in the back of the pocket (the blue line). These are two pieces, with their top edges following the other side of each dart.
The pocket lining follows the bottom line of the backs but its top copies the top of the pocket on the skirt. It looks a bit odd in this drawing but those two lines at the top should get seam allowance added to them to either side and they are essential when sewing this pocket.
And finally, you make the front pleat by adding width (about 14 cm in total) at 4 cm from the front edge (which is 2 cm from center front).
I didn't draw out the pocket flap but that's simply a semi-circular piece with its top as long as the top edge of the pocket.
When sewing the pockets, start by making the flaps.
Then, stay-stitch the corners of the skirt pockets at the stitching line. Place the flaps (wrong side of flap to right side of skirt) so that they reach exactly from corner to corner (on those stitching lines) and sandwich the pocket lining (right side to right side of skirt) over the pocket flap. It is best to sew with the skirt on top, so you can follow the stay-stitching lines.
After sewing, clip the seam allowances on skirt and pocket lining to the corners and turn the lining to the inside. Press and understitch (don't topstitch).
Sew the seam on the pocket back. Pin and sew pocket back to pocket lining. In those vertical-ish bits at the top (right down to the corner), this new line of stitching should be exactly on top of the line of stitching which attached the pocket lining to the skirt.
And that's your stick-out pocket!