The phrase "gave run around" means to avoid or evade someone or something in a deceitful or annoying way. Some antonyms for this phrase include being straightforward, honest, and direct. Instead of giving someone the run around, one can provide clear and concise information or answers. Another antonym for this phrase is responsiveness. Being responsive means being attentive and prompt in addressing someone's concerns or questions. Overall, the antonyms for "gave run around" involve being truthful, forthright, and proactive in communication, avoiding any misleading or deceptive behavior.