The phrase "under hate" can have a variety of synonyms, depending on the context in which it is used. Some possible options include "amid animosity," "beneath animus," "submerged in loathing," or "buried in enmity." Other potential synonyms might include "suffused with antipathy," "weighted down with hostility," or "plagued by resentment." Ultimately, the best synonym for "under hate" will depend on the specific nuances and connotations of the original phrase, as well as the tone and message of the broader text in which it appears.