Here we explore the possibility of precise time keeping in quantum systems using athermal resources. We show that quantum measurement engineered reservoirs can be used as athermal resources to drive the ticks of a quantum clock. Two- and three-level quantum systems act as transducers in our model, converting the quantum measurement-induced noise to produce a series of ticks. The ticking rate of the clock is maximized when the measured observable maximally noncommutes with the clock's Hamiltonian. We use the large deviation principle to characterize the statistics of observed ticks within a given time period and show that it can be sub-Poissonian—quantified by Mandel's Q parameter—alluding to the quantum nature of the clock. We discuss the accuracy and efficiency of the clock, and extend our framework to include hybrid quantum clocks fueled by both measurements, and thermal resources. We make comparisons to relatable recent proposals for quantum clocks, and discuss alternate device implementations harvesting the quantum measurement engineered nonequilibrium conditions, beyond the clock realization.