Bear reign is a phrase that is often used to describe someone who is in a position of power or authority. It can also refer to someone who has a strong influence over others or has a dominating personality. Some possible synonyms for bear reign include hold sway, wield power, exert control, dominate, rule the roost, command, or preside over. These terms all convey a similar sense of being in charge or having a significant amount of influence. Depending on the context, some of these synonyms may be more appropriate than others, but they all capture the idea of someone who is powerful and influential.