"Give heave-ho" refers to the act of dismissing or getting rid of someone or something. Its antonyms could be "retain," "keep," "employ," "honor," "respect," or "admit." To retain is to keep or maintain something or someone, while to keep suggests an act of holding on to something or someone. Employ, on the other hand, suggests hiring or engaging someone's services. Honor and respect imply bestowing admiration or showing reverence to someone or something. Lastly, admit means to let someone or something into a place or group. The antonyms of "give heave-ho" all suggest positive actions towards something or someone, in contrast to the negative connotation of "give heave-ho.