First of all the nocking point must be higher then the arrow resting on your hand. On a long bow an angle of 90 degrees to the string plus 5 mm lowering on the bow handle is fine. For a horsebow shot when galopping I recommend the following solution:

Here my arrow has an angle of 90 degrees plus 10 mm lowering on the bow handle. Such a low arrow rest will prevent scratching even on horseback.
Second the feathers should be secured. Treemarks suggested tape or nylon. I dug out some pics to illustrate, perhaps some of you others have examples as well. Here is cotton string:

And here my favourite, because easy & fast, sanitary hemp with carpenters glue:

Tape should also be fine, but I have never tried it.