Vapor cell atomic clocks are widely appreciated for their excellent short-term fractional frequency stability and their compactness. However, they are known to suffer on medium and long time scales from significant frequency instabilities, generally attributed to light-induced frequency shift effects. In order to tackle this limitation, we investigate the application of the recently proposed auto-balanced Ramsey (ABR) interrogation protocol onto a pulsed hot vapor Cs cell clock based on coherent population trapping (CPT). We demonstrate that the ABR protocol, developed initially to probe the one-photon resonance of quantum optical clocks, can be successfully applied to a two-photon CPT resonance. The applied method, based on the alternation of two successive Ramsey-CPT sequences with unequal free-evolution times and the subsequent management of two interconnected phase and frequency servo loops, is found to allow a relevant reduction of the clock frequency sensitivity to laser power variations. This original ABR-CPT approach, combined with the implementation of advanced electronics laser power stabilization systems, yields the demonstration of a CPT-based Cs cell clock with a short-term fractional frequency stability at the level of 3.1 × 10 −13 τ −1/2 , averaging down to the level of 6 ×10 −15 at 2000 s integration time. These encouraging performances demonstrate that the use of the ABR interrogation protocol is a promising option towards the development of low drift CPT-based frequency standards. Such clocks could be attractive candidates in numerous applications including next-generation satellite-based navigation systems, secure communications, instrumentation or defense systems.