Introduction: Nurses seem to be persistently experiencing intense psychological repercussions, even after the official conclusion of the COVID-19 pandemic. In this cross-sectional study conducted after the end of the pandemic crisis, from 1 June 2023 to 30 June 2023, we evaluated the levels and explored the associations between anger, insomnia, and resilience among Greek nurses. Methods: A total of 441 nurses participated in an online survey and were invited to state their work experience, gender, and age and to complete the self-report measures of the Dimensions of Anger Reactions-5 (DAR-5), the Athens Insomnia Scale (AIS), and the Brief Resilience Scale (BRS). Results: Overall, 62.1% of the participants presented with positive scores on the AIS, and 41.5% displayed positive values on the DAR-5 scale, whereas 24.9% demonstrated scores indicative of low resilience on the BRS. A regression analysis revealed that 23.5% of the variance in the AIS scores can be attributed to the DAR-5 scores and 3% to the BRS scores. A mediation analysis confirmed the protective role of resilience, contributing as a negative mediator in the DAR-5 and AIS relationship. Conclusions: Screening for insomnia symptoms and anger issues among nurses after the end of the pandemic and implementing appropriate interventions is considered imperative to avoid long-term health consequences.