In the context of the New Normal and the VUCA (volatile, uncertain, complex, ambiguous) era, organisations face adjustments to the changes brought by the COVID-19 pandemic, especially the shifting to new work modes and configurations with their consequences on employees’ wellbeing, in terms of exhaustion, resignation, and quitting tendencies. This study, rooted in the psychology of sustainability and sustainable development, employs a primary prevention perspective to examine a relational factor, the leader–member exchange (LMX), which might shield employees from exhaustion and turnover intention. Specifically, we propose a double-chained mediation model to investigate how high-quality LMX fosters a positive adjustment to employees’ specific work modes, in-person or hybrid work, subsequently reducing employees’ feelings of exhaustion and their intentions to leave the organisation. A convenience sample of 257 Italian employees participated in this study by completing an online self-report survey. Hypotheses were tested using the PROCESS macro in SPSS 25.0 (Model 6). The results indicate that positive LMX and adjustment to the work mode reduce exhaustion and turnover intention; furthermore, they highlight the existence of a more complex dynamic linking LMX to turnover intention through a double-chained mediation of adjustment to the work mode and exhaustion. Indeed, higher LMX quality favours adjustment to the work mode, decreasing employees’ feelings of exhaustion and, in turn, their turnover intention. Specifically, the findings of this study add a novel contribution to the literature on the psychology of sustainability and sustainable development by emphasising the significance of positive LMX in becoming a factor of wellbeing and sustainability in the workplace through the promotion of the adjustment to both in-person and hybrid work modes. Organisations may benefit of this approach to LMX that, through the consideration of employees’ needs, may favour their adjustment to different work modes, thus becoming a sustainable LMX, and a promoter of employees’ wellbeing and retention.