Optical atomic clocks produce highly stable frequency standards and frequency combs bridge clock frequencies with hundreds of terahertz difference. In this paper, we propose a hybrid clock scheme, where a light source pumps an active optical clock through a microresonator-based nonlinear third harmonic process, serves as a passive optical clock via indirectly locking its frequency to an atomic transition, and drives a chip-scale microcomb whose mode spacing is stabilized using the active optical clock. The operation of the whole hybrid system is investigated through simulation analysis. The numerical results show: (i) The short-term frequency stability of the passive optical clock follows an Allan deviation of o-y(r) = 9.3 x 10-14r-1/2 with the averaging time r, limited by the population fluctuations of interrogated atoms. (ii) The frequency stability of the active optical clock reaches o-y(r) = 6.2 x 10-15r-1/2, which is close to the quantum noise limit. (iii) The mode spacing of the stabilized microcomb has a shot-noise-limited Allan deviation of o-y(r) = 1.9 x 10-11r-1/2. Our hybrid scheme may be realized using recently developed technologies in (micro)photonics and atomic physics, paving the way towards on-chip optical frequency comparison, synthesis, and synchronization.