Which instrument is primarily affected by a leak in the static system?

A leak in the static system primarily impacts the altimeter because this instrument relies on external atmospheric pressure to provide altitude readings. The altimeter measures the pressure outside the aircraft and translates that into altitude above sea level. If there is a leak in the static system, the pressure reading can become inaccurate or unstable, leading to faulty altitude indications.

In the context of other instruments, while the vertical speed indicator also uses static pressure to determine the rate of climb or descent, its readings can still provide some useful information even with a static leak, as it's based on changes in pressure over time rather than a steady state. The airspeed indicator and artificial horizon are not directly dependent on static pressure; airspeed indicators use pitot pressure combined with static pressure, and the artificial horizon relies on gyroscopic principles, making them less susceptible to issues arising specifically from static system leaks. Hence, the altimeter is the instrument most critically impacted by problems in the static system.