Hello Astrid. You have several very reliable options for binding minced meat patties without eggs, and they will hold together wonderfully in an air fryer.
The most traditional and effective method is a classic panade. To make this, simply soak breadcrumbs or small pieces of torn bread in a few tablespoons of milk, broth, or water for a couple of minutes until it forms a soft paste, then mix it into your minced meat. The starches trap moisture and create a soft, cohesive network that keeps the patties firmly together.
Another simple option is a starch binder. You can mix one to two tablespoons of cornstarch or potato starch with an equal amount of cold water and add it to the mixture. If you prefer a whole-food alternative, ground flaxseed works exceptionally well: whisk one tablespoon of ground flaxseed with three tablespoons of warm water, let it rest for five minutes until it thickens into a gel-like consistency, and blend it with your meat.
Finally, a helpful culinary tip is to make use of the natural proteins in the meat. Adding salt and kneading the meat mix by hand for one or two minutes helps extract myosin, a protein that naturally binds ground meat together. Shaping the patties and chilling them in the refrigerator for twenty minutes before placing them in the air fryer will also ensure they do not crack or break during cooking.