The phrase "hunt up" can mean to search for something, but there are several synonyms that can be used in its place. One alternative is to "look for" something, which is a simple and straightforward replacement. Another synonym could be "seek out," which implies actively searching for something until it is found. "Scour" is another option that connotes a thorough and exhaustive search. "Track down" adds a sense of determination to the search, which may be appropriate in the context of a difficult or elusive item. Finally, "fetch" could also work as a synonym, particularly if the item being hunted up is a specific thing that needs to be retrieved.