Despite being a Republican State, India is a member of the Commonwealth of Nations whose head is the British Monarch. This is because

India's decision to remain a member of the Commonwealth of Nations, while accepting the British Monarch as the symbolic Head of the association, does not compromise its status as a sovereign republic. In 1949, India declared its continuation in the Commonwealth through an extra-constitutional declaration that does not affect its sovereignty in any manner [1]. The Commonwealth is defined as a voluntary association of independent and equal sovereign nations [1]. Unlike the earlier 'British Commonwealth' which required allegiance to the Crown, the modern Commonwealth allows republics to remain members without acknowledging such allegiance [2]. The British Monarch serves only as a symbol of the free association of independent member nations and as the Head of the Commonwealth, a role that is symbolic and unifying rather than one of political authority over member states [4].

Sources

1. [1] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 88: Foreign Policy > fl i Links with Commonwealth > p. 609
2. [2] Indian Polity, M. Laxmikanth(7th ed.) > Chapter 5: Preamble of the Constitution > 1. Sovereign > p. 43
3. [4] https://carnegieendowment.org/research/2018/04/india-and-the-commonwealth-redirecting-the-relationship?lang=en