It was never explicitly established, but the end of Will You Take My Hand and the beginning of Brother provide pretty strong implication that Pike is the Captain they were headed to pick up.
First of all, the signals that kicked off Pike's new mission appeared two days before the Discovery's crew was honored with the medal ceremony we see at the end of WYTMH? and they were dispatched to Vulcan.
Second, Pike already had his 'introduction' to Discovery's crew planned and ready for public display, and had already been briefed on at least some of what they had gone through during the war, even if he didn't know the full story about exactly how they lost their previous Captain.