The phrase "upper hand" refers to having an advantage over someone or something. There are several synonyms for this term, which could be used in different contexts. For example, "dominance" refers to having power and control over others. "Advantage" indicates a favorable position in a competition or situation. "Superiority" suggests being better or stronger than something else. "Ascendancy" refers to a position of authority or influence. "Edge" suggests a slight advantage or benefit. "Lead" indicates being ahead of someone else. "Supremacy" refers to being in a position of ultimate power or control. These synonyms can be used interchangeably depending on the context and the desired tone.