The European Society of Intensive Care Medicine (ESICM) suggests nine quality and safety indicators of care for critically ill patients. The aim of the present study was to examine the Key Process and Outcome Indicators (KPOIs) chosen according to International Standard Organization (ISO) protocols in a Greek Pediatric Intensive Care Unit (PICU). Two structure, one process, and four outcome indicators were examined in a stepwise approach according to Observe-Plan-Do-Study-Act (OPDSA) cycles, in an observational four-year cohort study (2017–2020). Two structure indicators—that ICUs fulfil national requirements to provide intensive care and 24-h consultant availability were requirements for the creation of the PICU and considered standards of care. One process indicator—Standardized Handover Procedure was transformed from handwritten (2017–2018) into electronic form (2019–2020) and 100% compliance rates throughout the four years were recorded. 96, 85, 103 and 94 patients were admitted in 2017, 2018, 2019 and 2020 with median (IQR) Pediatric Risk of Mortality III-24 h scores of 10 (6.25–17), 10 (6–13), 8 (5–13) and 8 (6.75–12), respectively. Mortality rates were 24%, 11.8%, 17.5%, 16%, and Standardized Mortality Ratio (SMR) were 1.42, 0.92, 1.56 and 1.33, correspondingly. No early (<48 h after PICU discharge) readmissions were recorded for 2017 and 2018, only 1 in 2019 (0.8%) and none in 2020. Catheter Related Bloodstream Infection rates were 1.37:1000, 1.37:1000, 1.26:1000 and 1.39:1000 catheter days, respectively. Unplanned extubation rate was 10.30% in 2019 and 5.72% and 3.91:1000 ventilation days in 2020. In conclusion, ISO implementation of our unit was the trigger for internal PICU audit and external benchmarking. OPDSA cycles, following small steps at a time, in an iterate cycle of evolution, facilitated our actions. The majority of the KPOIs examined in our study was within international PICUs reference values.