The answer to 'how to unclog shut-off valve' is to first turn off the water supply to the valve, then use a plumber's wrench or pliers to carefully remove the valve handle. Next, use a plumber's auger or snake to clear any debris or blockage in the valve. Be sure to turn the water back on slowly and check for any leaks once the valve is unclogged.
Shut-off valves can become clogged over time due to mineral buildup or debris in the water system. Unclogging the valve yourself can save you the cost of calling a plumber, but it's important to take the proper safety precautions. If you are unable to clear the clog or the valve is damaged, it's best to call a professional plumber to assess and repair the issue.