Pompous gait refers to a walking style that is exaggerated and often perceived as arrogant or self-important. Some synonyms that could be used to describe this type of gait could include swagger, strut, or sashay. Each of these words conveys a sense of confidence and self-assurance, but can also be seen as overly showy or conceited. Other options might include prance, parade, or march, which could be interpreted as more formal or ceremonial in nature. Ultimately, the choice of synonym will depend on the tone and context of the sentence, as well as the intended impression of the speaker or writer.