**1. Introduction**

Leadership is one of the most important phenomena in management research and practice, leading to a large body of theoretical and empirical work [1, 2]. Their impact on their organizations' performance cannot be overstated. Leaders are responsible for their organization's success and failure. Influencing others is leadership [3]. Leadership is a major factor in employee performance [4, 5]. Leadership stimulates employee innovation and inventive work behavior [6, 7]. Organizations are focused on refining their current processes and offers and strengthening and sustaining their market position [8]. In tough circumstances, organizations must innovate and adjust procedures to boost innovation performance [9]. Leadership is a key predictor of organizational innovation and the level of innovation support in an organization.

Each organization's development and present operation are dependent on the traits of its leaders. In addition to having a clear vision and effectively communicating it, managers of organizations need to have people-motivating abilities. It is evident that effective leadership is required [10]. However, over time, the definition of "suitable leadership" has evolved [11]. The way organizations should be managed is being impacted by changes in the business environment, including new stakeholder needs. The global shift toward sustainability is another example of such a development [12]. Traditional leadership was only focused on making money, and conventional conceptions of development—which persisted until the 1970s—evaluated development within the context of economic expansion [13]. The three interconnected pillars of sustainable innovation, innovativeness and organizational innovation performance must be balanced by current leaders [14].

This chapter explores many articles that discuss leadership styles and organizational innovation to better understand this link and draw a unique conclusion. This analysis will assist organizations and decision-makers choose the best leadership style to boost innovation and get a market edge. According to Amundsen et al. [15] "Leader support" is the most critical requirement for innovation success. Arshad et al. [6] say management support drives innovation for two reasons. First, employee participation in strategic innovation decision-making requires managerial backing. Second, it could mean coaching employee initiatives during ideation and decision-making. Smith et al. [16] identified leader support as a critical antecedent of creativity and innovation, saying that management behavior and creativity demand more attention. Studies have shown that subordinates need leadership support to innovate [17, 18]. Despite our theoretical grasp of leadership's impact on innovation, we lack a comprehensive understanding of how specific leadership styles might encourage or hinder sustainable innovation. Smith et al. [16] propose a favorable influence of leader support on creativity and innovation. However, different leadership styles have varied benefits and drawbacks [19]. How will leadership styles affect sustainable innovation?

This chapter examines how leadership styles affect innovation among leaders and subordinates. Which style delegated authority to subordinates? [15, 20]. The innovation described above presents some traits of a suitable leadership approach under the context of current business operations. Although some authors (e.g., [21–24]) emphasized that transformational leadership contributes to broadly defined sustainable innovation by influencing responsible practices and behaviors, others (e.g., [25]) explored the benefits of servant leadership. Others have written about sustainable leadership, such as Avery and Bergsteiner [26] and Iqbal et al. [27]. Sustainable leadership is a marginalized and underdeveloped topic, according to a literature analysis on the effectiveness of sustainable human resource management done by Santana and Lopez-Cabrales [28]. According to Kjellström et al. [11], leadership in general is a complex phenomenon that requires further investigation. The purpose of this study is to identify and explore the leadership styles (types) that positively influence the performance of sustainable innovation, both numerically and qualitatively. This will further the field of "leadership-sustainable innovation" research by analyzing, contrasting, and synthesizing earlier findings [29]. For the purpose of this study, the following research questions were formulated: We studied these competing leadership styles because of their clashing qualities. We answer these questions.

RQ1: Which leadership style best fosters sustainable innovation?

RQ2: Which leadership theory is most helpful for creativity by leaders and subordinates?

*Leadership and Sustainable Innovation: A Systematic Literature Review DOI: http://dx.doi.org/10.5772/intechopen.109150*

RQ3. Future study on leadership and sustainable innovation?

By concentrating on the implications of recent work on innovation for sustainability and leadership styles in the service industries, the current study fills in these gaps. In contrast to earlier review studies, this study highlights the key themes in the various leadership innovations and styles that have been described in the literature. We do this by offering several taxonomies, summarizing recent research, and perhaps moving academic efforts away from pure inquiry and toward a more methodical approach. To conduct a comprehensive thematic analysis of the existing literature, it uses both quantitative and qualitative methodologies. The results are used to identify what is now known about sustainable innovation and what needs further study from a leadership viewpoint. The study starts off by providing a summary of current leadership research before zeroing in on the literature on innovation. The chosen technique is presented in the following parts, together with a thorough analysis of the findings, conclusions, and suggestions for further study.
