There are plenty of ways to do that.
Option A. From the Category itself.
Create a menu item of type Akeeba Ticket System, Category (or Akeeba Ticket System, Categories).
This presents existing tickets in the category, along with a New Ticket button which creates a new ticket into that category; no selection necessary.
Option B. With a menu item.
You can create a menu item of type Akeeba Ticket System, New Ticket.
When you do that, there is a Category option in the Details tab. Click on Select next to it to select your (sole) category.
Using this menu item will always create a ticket in this category.
What you can and cannot do
You cannot completely remove the Category field from the ticket form. This is not a limitation of Akeeba Ticket System; it is a limitation of Joomla's Fields feature (a.k.a. custom fields). For them to display on the page there must be a Category field in the form so that Joomla! knows which fields to display. Here's the kicker. Joomla cannot know if there are any fields to display unless there is a Category field. Therefore, we cannot remove the Category field because the condition for removing it depends on the core Joomla Fields feature which depends on the Category field's presence. It's a chicken and egg problem.
Nicholas K. Dionysopoulos
Lead Developer and Director
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