StevePage
Okay, I see now. We don't have such a concept of approvals, etc. in osTicket at this time. We don't have any core plugins that offer this either but maybe you can search online for any community-made plugins. Just proceed at your own risk as no 3rd party code is ever verified nor recommended by us (the core osTicket development team).
I will say that you can Transfer Tickets from one Department to another; so they can go to an "Approval" Department (based on certain criteria) and you can set only "approving" Agents to have access to this Department and they can then "approve" the Ticket and Transfer the Ticket to the appropriate Department of Agents. Tickets can also be assigned to an individual Agent or Team of Agents outside the Ticket's main Department. You can also Refer Tickets to other Departments where the Referred Department can only view and add Internal Notes to the Tickets.
You can review our Documentation here that covers the features, how things work, etc.:
Cheers.