The Kaelon sun was the primary of its system. Located somewhere in the Alpha or Beta Quadrant, Kaelon II, the homeworld of the Kaelon, orbited this sun in the system's habitable zone. Beta Praxillus, a star in the Praxillus system, was similar to this star.
The Kaelon sun was dying, leading generations of Kaelon scientists to research various methods of stabilizing stellar energy reactions. The sun was transforming from a yellow dwarf to a red giant and was expected to destroy or sterilize Kaelon II by the 2390s. (TNG: "Half a Life")
This sun was only mentioned in dialogue.