You cannot have branch circuits from another service/panel (hospital) supplying the clinic. Im assuming alot things here, but if there are 2 seperate services there is probably 2 meters, so the clinic would be using the power from the hospital, and they (the hospital) would be paying for it?? You cant do that.
Also, it appears that single 'emergency' circuit from the other panel would be an additional disconnect for that clinic, because you would have cut off that breaker to turn off all the 'ungrounded' conductors supplying that building.