Are you asking for a way to create a new ticket form un the ui?
If your answer to this is Yes, then you can alter the ticket opening experience by putting forms on Help Topics. So when someone selects the Help Topic of "New Starter" it displays a form for all the fields that you want to add, or if they select a Help Topic of "Leaves" then it displays yet another form.
Or are you asking for a way to put a form on a separate web site?
You would have to write a custom HTML (and other language) script that interfaces with the Ticket API. This would let you make a separate page for creating a ticket for new starters and one for leaves.
