(Although I would try to cover them as much as possible) I have some tattoos on my wrist from my jahil youth days and I want to study Howza in Qom InshAllah. I know that scholars must adopt a certain dress and behavior. I was worried my tattoos would prevent me from becoming a student of knowledge. Would it?

No not at all these all are whispers of Shaitan. You must follow what you have determined about your life in the way of Allah. Don’t think what people will say. Hawza has long vision nobody will bother you inshallah.