Optical atomic clocks are moving toward deployable systems, with commercial instruments entering the 10⁻¹⁷ fractional-frequency-instability regime. Transferring this performance to accessible microwave and radio-frequency signals requires compact optical frequency combs that preserve long-term stability during frequency division. Integrated Kerr microcombs have opened a new era in chip-scale precision metrology, enabling optical-frequency division and low-noise microwave generation. Yet, whether they can robustly preserve the stability required by state-of-the-art optical lattice and single-ion clocks over hour-long timescales remains an open question. Here we demonstrate that a hybrid passive-active stabilization of a Kerr microcomb, combining injection-locking of one tooth with active stabilization of a second, freely selected tooth through pump-frequency actuation, can indeed satisfy the metrological requirements at the highest level. The separated control channels effectively orthogonalize stabilization of the two microcomb frequency degrees of freedom while leaving the pump frequency unconstrained. A continuous five-hour measurement, without drift removal, yields a residual relative instability of 1.4×10⁻¹⁶ at 1 s and 2×10⁻¹⁸ at 4000 s on an out-of-loop tooth. We further show that the residual instability remains unchanged as the injection power is varied over 14 dB, demonstrating robust operation across a broad locking range. These results bring integrated microcomb stabilization into the residual-noise regime required to preserve the long-term performance of emerging optical lattice and single-ion clock systems.