The antonyms for the phrase "fill to brim" include "empty," "drain," "evacuate," "deplete," "remove," "scant," and "starve." These words convey the opposite of the concept of filling something, whether it be a container, space or time. For example, instead of filling a glass of water to the brim, one can empty or drain it completely. Alternatively, if someone desires to deplete or remove something from a container or space, they could do so, rather than filling it up. Overall, understanding the antonyms of "fill to brim" provides a range of options for describing the opposite action.