Brent was sent on a rescue mission to look for Taylor and his crew. This makes absolutely no sense for myriad reasons, including:
1) The first
Planet of the Apes (1968) film specifically states that the crew was traveling near the speed of light. As such, decades or even centuries must have passed on Earth. Since the scientists who sent them on the mission would know, why would they send a rescue for a someone who they would never live long to "miss?" (the only way it would make sense is if Brent and his Skipper had been following Taylor's ship at a distance in case they needed assistance, and just never mentioned on the first film).
2) Where would they have "looked" for Taylor's mission? Space is a vast place and even sending a ship along the same route as Taylor would be no guarantee that they would ever find his vessel.
3) Even if Brent left the day after Taylor did, it would likely be decades or centuries before he caught up to Taylor, in which case the people who sent them both would be long dead before they knew if either mission was successful.
There was no need to sent Brent on a "rescue" or recovery mission as it would have taken place decades or centuries later than it would possible or necessary.