The phrase "brings up rear" can be considered an idiomatic expression that means to be at the back of something or to be the last in line or the last to perform. Antonyms for this phrase can vary depending on the context of use. In the case of a race or competition, some antonyms could be leading, coming first or being in front. In a line or a queue, the antonyms would be being at the front, at the head or leading the line. In general, antonyms for "brings up rear" would be any expression that connotes being in front, coming first, or leading the way.