The phrase "up to one's ears" implies a state of being overwhelmed, deeply involved or fully committed. Its antonyms are those words which convey the opposite meaning, such as "completely free," "disengaged," "idle," "leisurely," "uninvolved," and "unoccupied." When we use the phrase "up to one's ears" it generally suggests that someone is feeling burdened or consumed by some circumstance, like work or stress. So, its antonyms imply a state of ease or relaxation. For instance, if someone says they are up to their ears in work, the opposite meaning of it is that someone is free from work obligations and enjoying a leisurely time.