L_Hurren
Mainly though, the Department needs to allow assignment to the intended Agent. Each Department has a setting called "Ticket Assignment" that controls who can be assigned to Tickets within the Department. If set to "All" anyone can be assigned (non-Department Members, Primary Members, and Extended Access Members), if set to "Primary Members" then only the Primary Members can be assigned, and if set to "Department Members" then all Primary and Extended Access Members can be assigned.
Other than that the Agent obviously has to exist, has to be Active (ie. not Locked, etc.), and must not be in Vacation Mode.
Cheers.