The phrase "kept one's distance" refers to maintaining a safe or emotional distance from someone or something. Antonyms for this phrase include drawing closer, closing the gap, approaching, embracing, and engaging. When we draw closer to someone, we reduce the emotional or physical distance between ourselves and that person. We may embrace or touch them, which can create a sense of closeness or intimacy. Closing the gap refers to reducing the distance between ourselves and a particular goal or objective, while engaging with someone means interacting with them in a meaningful way. In summary, the antonyms for "kept one's distance" imply a desire for closeness, intimacy, and meaningful interaction.
