There are several synonyms for the phrase "secret advantage" that can be used in various contexts. One such word is "edge," which implies having a subtle advantage that is not immediately noticeable. Another synonym is "upper hand," which suggests having dominance over a situation or person. "Trump card" is also a popular phrase that denotes having a hidden advantage that can be used to gain leverage in a situation. In addition, "privilege" can also be used to describe a secret advantage, especially in situations where power and influence are involved. Ultimately, the choice of synonym depends on the intended tone and context of the message.