Cap holder for belt

Functionally similar to a carabiner.
(You can just as well use a carabiner.)

Make a leather strip that's about 1,5 cm wide and 25–27 cm long.

This strip loops around the belts just above two times.
Start just below the top of the backside of the belt and loop it around the belt.

Use two revits to join the two layers behind the belt.
As an (untested) alternative, you could use push button to allow it to be
move around more or removed without removing your belt.

Make sure you have enough slack on the front side for the
cap's strip, then add a push button to join the two layers
on the front side.

The remainder of the strip is tucked away behind the belt.
If you only made the strip 22 cm long, you would have enought
extra after the push button to easly open it without having
to tuck it away behind the belt.