Wiktionary
a. (context of an Eastern Orthodox or Eastern Catholic monastery English) stauropegial.
Wikipedia
A stauropegic monastery, also rendered stavropegic, stauropegial, or stavropegial (from stauros "cross" and πήγνυμι pegnumi "to affirm"), is an Eastern Orthodox or Eastern Catholic Christian monastery subordinated directly to a Patriarch or Synod, rather than to a local Bishop. The name comes from the Byzantine tradition of summoning the Patriarch to place a cross at the foundation of such monasteries.
Stauropegic monasteries are distinguished from the greatest monasteries, called lavras, and from the patriarchal metochions, where the patriarch serves as a parish priest. The metochions of the Patriarch of Moscow are the Vysokopetrovsky Monastery and Nikolo-Perervinsky Monastery.