In light of future work challenges, actual human resource management (HRM) needs to be redesigned, including long-term development, regeneration, and renewal of human resources, passing from consuming to developing human resources by incorporating the concept of sustainability. Thus, sustainable HRM is seen as an extension of strategic human resources, presenting a new approach to human resource management. The labor market is constantly changing, atypical work acquiring a significant relevance, especially in these current times of coronavirus crisis restrictions. In Romania, promoting the law of teleworking transformed labor flexibility into a topic of interest, and became an increasingly vital requirement for employment and a motivating factor for Romanian employees. In such a context, this paper aims to investigate the link between employee development and worktime and workspace flexibility as relevant characteristics of sustainable HRM, job satisfaction and job performance among Romanian employees in order to identify how to redesign HRM in the face of “future work” challenges. Additionally, the paper aims to examine the impact of different types of flexibility—contractual, functional, working time, and workspace flexibility—in order to highlight the relevance of employee development and employee flexibility as important aspects of sustainable HRM in increasing the overall level of employee job satisfaction. In order to make this possible, an “employee flexibility composite indicator,” which takes into account different types of flexibility, has been developed using feedback from Romanian employees, which was gathered by a national representative survey using multiple correspondence analysis. Furthermore, the impact of both individual and employee flexibility on overall level of job satisfaction has been quantified using binary logistic regression models. Within the research, there is a particular focus on the impact of new types of workspaces (flex office, co-working, total home office, partial home office—FO, CW, HOT, HOP) on job performance, job satisfaction, organizational performance, professional growth and development, social and professional relationships, and personal professional performance as well as on the overall level of work motivation. The empirical results revealed that these new types of workspaces are highly appreciated by employees, generating a growing interest among them. Partial home working, the mix between working from home and working in a company’s office, has been considered an optimal solution in increasing organizational performance, social and professional relationships, learning and personal development, and the overall level of work motivation. The results of the multiple correspondence analysis highlighted a medium level of flexibility among those Romanian employees interviewed, with only one third of them exhibiting high levels of flexibility. The empirical analysis of logistic regression analysis pointed out the role of functional flexibility, working time, and workspace flexibility along with the flexibility composite indicator in increasing the level of job satisfaction in employees. Therefore, if the challenge is to redesign the actual human resource management in order to include the concept of sustainability, attention needs to be on a combination of employee development-flexible time and flexible places, leading to an increase in both employee job satisfaction and organizational performance as important outcomes of sustainable HRM.