In order to express the idea of waiting for a certain situation to resolve itself, there are a number of different synonyms for the phrase "wait out." One potential alternative expression is to "ride out" a particular situation, which suggests a sense of perseverance in the face of difficulty or adversity. Another similar choice might be to "weather" a particular situation, which implies that one is simply enduring it until conditions improve. Other possible options might include "stay the course," "hold steady," or "bide one's time," each of which suggests a certain level of patience and persistence in the face of uncertainty or difficulty. Ultimately, the choice of wording may depend on the individual's personal style and the specific context in which they are using the phrase.