My dad has a long habit of combing his hair every few hours, but all his shirts' and pants' pockets are open as in this picture: no zippers or buttons to fasten the pocket.
While on the job, he can't carry a purse. It's obviously unproductive to add zippers to all his clothings' pockets. Too many combs have slid out of pockets, as he must frequently sit and get up. A retractable ski pass holder 'Skipasshalte' doesn't appear to befit combs.
A shorter comb will stay in place better. It will tend to sink to the bottom of the pocket and get somewhat suck, which is a good thing.
If he can't find a shorter comb, get a normal black plastic comb and saw it in half (since this is a lifehacks community!). Sand down the sawed edges so there aren't any jagged edges.
Tie the comb to a small string, and attach to the other side a safety pin. You can then attach that pin to the shirt.
Combs exist with a clip, similar to a pen, for helping hold a comb in the pocket:
Perhaps if you do not wish to purchase such, you could manufacture a similar one by attaching a clip off a pen lid, to an existing comb. The exact method of attachment would depend on the clip and the comb; perhaps if you find some you could post pictures of them up for more advice
Attach a small fishing weight to a small comb by drilling a hole in the comb and using a key fob key ring. Put the comb in the pocket heavy side down. Hold the weighted end when using the comb