Making potato pancakes without egg I am wanting to make these Kartoffelpuffer, which is german for potato pancakes. I am looking to use this recipe https://www.allergygirleats.com/potato-pancakes/

The ingredients are as follows:

Ingredients

500g Parboiled Potatoes

1/4 cup White Onion - finely chopped

1/4 tsp Salt

1 tbsp Potato Starch

1 Egg

1 tbsp Ghee

1 tsp Olive oil

This is a gluten free recipe but I was also wondering if I could make it vegan as well/dairy free? Which ingredients here would fall under vegan or dairy free?
I  saw the eggs, is there any substitution for that?

Thanks. (Need it more vegan than dairy free, that's the least of the priorities) Thanks!
The non-vegan ingredients are the egg and the ghee (clarified butter, browned to develop the nutty flavours).

For the ghee you can substitute the same quantity of olive oil, possibly with some loss of flavour.

The egg is harder to replace. You could try a commercial egg replacement: these are powdered starch (one product uses potato and tapioca flour, so is gluten free) with assorted emulsifiers. A substitute widely recommend on the web for savoury pancakes is a gel made from flax or chia seeds: mix 1 tablespoon of seeds with 2.5 tablespoons of water and leave for 10 minutes for the seeds to fully hydrate.