What instrument would fail if the static port is clogged?

If the static port is clogged, all pitot static instruments will provide incorrect readings.

Many aircraft will have an alternate static port to provide an alternate source of static pressure. If the static port becomes clogged, the airspeed indicator will under report speed when climbing and an over report speed when descending. This error is the opposite when the pitot tube is clogged. The vertical speed indicator will show zero rate of change with a clogged static port. The altimeter will remain constant at the altitude reading when the blockage occurred.

Reference(s):

FAA-H-8083-25A Pilots Handbook of Aeronautical Knowledge pg. 8-10

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