Take applications without opening a ticket for each one. Post a panel with an Apply button, and a member who presses it fills in your form: up to five questions, each a short answer, a longer answer, or a pick from a list. The answers go to a staff channel you choose, where staff press Accept or Deny. A deny can carry a reason, and the member gets a DM with the answer either way. Accepting can give a role.
You can limit a form to members with certain roles, let more roles review besides members with Manage Server, and make a member wait some days after a deny before they apply again. A member has one application open per form at a time. Packet keeps an application for 90 days after it is decided.
(Configure → Forms.)