A Center Controller reported a military UAS flew an unexpected route outside of their designated airspace. The reporter had to vector another aircraft to avoid a confliction with the UAS.

Narrative

Aircraft X; a drone; was climbing off of ZZZ. The normal operating procedure is they climb within Special Use Airspace until reaching class A airspace; then proceed on course. We sterilize that airspace upon seeing the departure. Aircraft Y departed ZZZ1 enroute to ZZZ2. We called ZZZ approach and assigned a 180 heading to avoid being in confliction with Special Use Airspace. The heading was assigned and both aircraft were climbing. After both aircraft had checked on; we waited for Aircraft Y to be greater than 3 miles from the Special Use Airspace; then issued a turn; I believe a 250 heading. Meanwhile Aircraft X was climbing south; and on the very south end of Special Use Airspace. They then continued to fly southbound and we had flashing between the 2 aircraft. We turned Aircraft Y immediately to a 180 heading. Then directed Aircraft X to return to Special Use Airspace to do their climb to class A. The aircraft at the closest point were 5.9 miles and 700 feet. Prior to turning back to the Special Use Airspace; Aircraft X questioned their approval to climb on a Ground-Based Sense-And-Avoid (GBSAA) departure. No coordination was done from ZZZ approach to say the aircraft was going to be doing that. We have a Letter of Agreement (LOA) with Aircraft X; there is not a mention of this procedure; so we have no idea what that departure actually is. Our assumption is they will comply with their LOA and climb within Special Use Airspace. We have no information on what a GBSAA is at the sector; nor do we have any paperwork that we have access to in the sector that tells us what that is. If that is what the drone wants to fly; we need to be aware of that as they depart. There needs to be a standard procedure all of the drones out of ZZZ follow. We have 4 different units flying drones; and they can not all operate differently with their own special departure procedures. The pilot; nor ZZZ approach ever mentioned they were on this departure. The only mention was in their remarks. Again; we have no idea what that departure procedure is.