I need to watch the scene again, but can anyone confirm whether Rand was on the bridge for this scene, or not. Maybe she was supposed to be there per the script, but something happened during shooting and Leslie was swapped in? This is too similar to a later scene where Kirk orders Rand to take the helm...I suspect script confusion/error or film editing. Maybe @Maurice has the story.
(I thought I remember that Spock gave a slight hand signal to Leslie's position, too?) Another thought is that Spock wanted Rand (if she was really there) to take over Leslie's Engineering Station as Leslie raced to the helm. Since she seems to be off camera in the TrekCore screencaps, then manning the engineer station is consistent since this station was off camera, too. In any event, after Riley leaves the bridge, Uhura takes over navigation. Later when Leslie succumbs:SPOCK: Why isn't Mister Sulu at this station?
RILEY: Magnetic pull compensated for, sir. Orbit steady.
SPOCK: Take over here, Rand.
RAND: Yes, sir.
SPOCK: You haven't answered my question. Where is Mister Sulu?
RILEY: Have no fear, O'Riley's here. One Irishman is worth ten thousand of you
SPOCK: You're relieved, Mister Riley. Lieutenant Uhura, take over this station.
UHURA: Yes, sir.
RILEY: Now that's what I like. Let the women work too. Universal suffrage.
KIRK: Get him out of here.
RAND: I would have gotten here sooner, sir but Crewman Moody stopped me in the hallway.
KIRK: Take the helm.
RAND: Sir?
KIRK: Take the helm!
RAND: Yes, sir.