The phrase "kicks up one's heels" means to enjoy oneself by letting loose and having fun. The antonyms for this phrase convey a sense of restraint and seriousness. Such words include 'restrain', 'constrain', 'conform', 'comply', 'abide', 'comport' and 'adhere to'. It implies a lack of freedom and expression. These words describe a scenario where a person is unable to indulge and have fun due to various reasons. For instance, when conducting serious business, it's crucial to stay restrained and conform to certain rules and regulations. Therefore, antonyms of "kicks up one's heels" describe a disciplined, serious, and restrictive state rather than a liberated and fun state.