Is it possible to set the ticket form based on agent group?
At this time, it is not possible to assign or associate a ticket form with an agent group or hide ticket forms from certain agents or agent groups.
There are a couple workarounds for certain aspects of this. While it is not yet possible to restrict forms by group, it is possible to set the form on a ticket based off the assigned group using custom triggers.
Additionally, there is a Zendesk Labs app that would allow you to make certain fields required, hidden, or read-only for a group of agents (based on what groups they are in). You can read more about this app here: Managing Ticket Fields for Agent Groups.