Private property was anything owned by private individuals, rather than a government or organization.
In 2266, Harcourt Fenton Mudd complained that the Denebians had no respect for private property after one of their patrol ships fired on the spaceship he stole from them. (TOS: "I, Mudd")
In 2366, "Kevin Uxbridge" informed a rescue party from USS Enterprise-D that they were on (his) private property and demanded to know their reasons for being there. (TNG: "The Survivors")
Some astronomical bodies were privately owned, such as the planet Holberg 917G (owned by "Mister Brack", aka Flint) (TOS: "Requiem for Methuselah") and a moon, owned by Quark's cousin Gaila. (DS9: "Civil Defense", "The Way of the Warrior")
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