The phrase "quest for" can be replaced with several synonyms depending on the intended context. It could be replaced with "pursuit of", "search for", "hunt for", "quest after", or "chase for", among others. All of these synonyms imply a desire or an effort to obtain or achieve something. "Pursuit of" often refers to a personal goal or aspiration, while "search for" and "hunt for" are often used when looking for something specific, like a lost item. "Quest after" suggests a more dedicated, adventurous search, while "chase for" can be used to describe a more intense pursuit. Ultimately, the choice of synonym will depend on the specific context of the sentence.