This study integrated research on competitive psychological climate (CPC) and successful career development within transactional stress theory and the job-demands resources model. The theoretical model assumed two different processes from CPC at work that might either foster or hamper career success. Specifically, CPC might be positively related to work engagement (motivation-enhancing path, CPC appraised as challenge) or burnout (energy-decreasing path, CPC appraised as hindrance), which then should be positively or negatively related to objective and subjective career success, respectively. High versus low leader-member exchange relationships are assumed to moderate the relationships between CPC and work engagement and burnout. In Study 1, we tested the theoretical model within a sample of 808 academic scientists from different research fields in Germany. By doing so, we applied conditional indirect effects analyses within a path-modeling framework. The results largely supported the theoretical model, and showed that CPC is positively related to the number of publications and career satisfaction via work engagement under the condition of a high LMX quality. By contrast, CPC was negatively related to career satisfaction via burnout under the condition of a low LMX quality. Within Study 2 and an additional independent sample, results showed that these pathways are explained via hindrance and challenge appraisals of CPC. We discuss these results against the background of competition-based HR systems, as well as the integration of challenge–hindrance frameworks in career developmental research.