Find the supported option
A professional can check whether the existing cable has an unused conductor, whether the correct common connection is available, and whether a new cable or supported power accessory fits the system. An unused wire at one end is not proof that it is usable at both ends.
Google's Nest guidance identifies a C wire or a compatible power accessory as possible solutions for certain installations. It also makes the requirement dependent on the thermostat and system. That is a product example, not permission to add any adapter to any furnace. Nest common-power guidance.
Ask the installer to compare the complete options: keeping the present thermostat, choosing a compatible thermostat with different power needs, installing a supported accessory, or adding the proper cable. Include the features you want to retain, such as independent fan operation and heating stages (the available heat-output levels).
Give the technician useful information
Share the thermostat's exact model, furnace model from an existing record or accessible label, current error message, and what changed before the trouble began. Existing installation photos can help. Do not open powered equipment to gather a better picture, touch terminals, or test the circuit with a jumper.
A label reading C can be misleading on a proprietary communication system. Compatibility depends on function and documentation, not just a matching letter or wire color. Google compatibility guidance.
Check the result, not just the screen
After any approved installation, ask the technician to verify stable thermostat power and every supported heating, cooling, and fan function that applies. A display that lights up does not show that the whole system is correctly controlled.
Your next step is to request a supported power plan tied to the exact thermostat and equipment, with the needed work and feature tradeoffs stated before you authorize it.