An inheritance was a sum of money or property that passed to an individual upon the death of another.
The novel Hotel Royale had a subplot about a woman who was conspiring with an older man to murder her husband while wasting her inheritance. (TNG: "The Royale")
In the distant past, the Sky Spirits decided to give the Inheritors a genetic bonding to enable them to take care of Earth better. (VOY: "Tattoo")
In 2374, Odo described a cargo load of Livanian beets as Quark's inheritance from a believed-to-be-dead Morn. Later, Nahsk and Krit hoped to collect on the "deceased"'s outstanding debts. (DS9: "Who Mourns for Morn?")
In 2376, while riding in a horseless carriage with Seamus in the Fair Haven holoprogram, Tom Paris attributed his ability to afford the vehicle to an inheritance from his grandfather on his mother's side, who was an aristocrat. (VOY: "Spirit Folk")
Some positions could also be inherited.
In 2267, Leonard James Akaar inherited Akaar's position as Teer of the Ten Tribes of Capella IV. (TOS: "Friday's Child")
In 2373, the Regent of Palamar bemoaned Nassuc's betrayal, saying that eventually she would have inherited his empire. (DS9: "Business As Usual")
Also that year, Demmas inherited the position of Autarch of Ilari from his deceased father. (VOY: "Warlord")