We report on the operation of a coherent population trapping (CPT) microcell atomic clock using a pulsed Ramsey-like interrogation. The Ramsey-CPT sequence, defined by two-step optical pulses separated by a free-evolution dark time, is produced by switching on and off the output power of a low-power vertical-cavity surface-emitting laser, through direct modulation of its driving current. High-contrast and narrow Ramsey-CPT fringes are detected without the use of any external optical modulator stage. We demonstrate closed-loop operation of the clock based on high-speed digital signal processing implemented in a field programmable gate array board. The clock's short-term fractional frequency stability is 1.3 × 10−10τ−1/2 until 2000 s. A power light-shift coefficient of 8 × 10−11/μW, in relative value, is obtained for a dark time of 150 μs. This value is about ten times lower than in the continuous regime. These results show the feasibility of fully integrated atomic clocks based on Ramsey spectroscopy, which could provide enhanced long-term stability.