A power supply was a system that sent energy to something.
In 2152, after Commander Charles "Trip" Tucker and Arkonian pilot Zho'Kaan separately crash landed on a moon where they became stranded together, Tucker suggested he could cannibalize the power supply from a nearby Arkonian transceiver in order to power up a transceiver from Shuttlepod 1, so they could transmit a distress call. (ENT: "Dawn")
In the final draft script of "Dawn", this term wasn't specified, with the word "tech" written instead.
In 2374, Seven of Nine and Harry Kim worked on the systems of Astrometrics in Jefferies tube 32B. After Seven aligned the optical assembly properly, she was ready to access the main power supply. (VOY: "Revulsion")