The second season of Star Trek: Discovery is definitely going to need at least one version of the iconic Spock, but there's more than one reason it's highly unlikely Zachary Quinto would board the CBS All Access series.
At the end of Star Trek: Discovery's first season, the titular Federation starship was on its was to Vulcan to meet pick up its new captain when it received a message from another starship - the USS Enterprise. Discovery takes place roughly a decade before the events of the original series, so the ship is under the command of Captain Christopher Pike (who will be played by Inhumans refugee Anson Mount), not James T. Kirk; but as we know from the TOS episode "The Menagerie," Spock is already serving on the Enterprise by this point. The look exchanged in the finale between Sarek and Michael Burnham - Spock's father and adoptive sister, respectively - should confirm that fact for any unsure viewers.
Discovery's producers have confirmed Spock will play a role in Season 2, though they've remained cagey about how exactly he'll be portrayed. Star Trek: Discovery director and The Next Generation star Jonathan Frakes seemed to confirm the longstanding rumor that we'll see Spock in flashback as a young child growing up with Burnham, but no one is spilling on how the show will deal with the contemporary version of Spock on the Enterprise.
Some fans are holding out hope that Zachary Quinto - the Spock of the three J.J. Abrams-produced Star Trek reboot films - will temporarily jump to the small screen to fill the Starfleet boots originally worn by the late, great Leonard Nimoy. This seems unfeasible for a few reasons. The most obvious is that Quinto is an active movie star in his own right; he doesn't actually have that much on his plate at the moment and could theoretically make it work schedule-wise, but he might be reluctant to take part in a series on a streaming service so few people even get at this point. There's also the question of how much of a boon it would be to the show; Discovery takes place in the Prime timeline, the continuity that was abandoned by the Abrams films in which Quinto stars. There's been no shortage of Star Trek fan outrage regarding the alternate universe timeline over the last decade, and there are still a surprising number of fans who don't even consider the Abrams films to be "real" Star Trek.
But the most compelling reason a Quinto guest stint seems unlikely is also the most depressing, real-world one. CBS and Viacom - once a single corporate entity, now the owners of the TV and film rights to Star Trek, respectively - are currently embroiled in a messy legal battle, with competing forces within CBS squabbling over a potential merger with the currently weaker Viacom. It seems highly unlikely that either company would be particularly excited about collaborating with the other right now, even if one were to put aside the fact the two sides have been arguing over who controls which aspects of Star Trek for the better part of a decade; the corporate maneuvering is said to be the reason Nicholas Meyer's Khan series is on indefinite hold.
Star Trek: Discovery has put itself in an incredibly tough spot regarding Spock. If someone other than Quinto plays the part, it's going to seem like an unnecessary recast of a character only two men have played over the last 50 years; if the adult version simply doesn't show up then the season finale tease is going to seem like a cheap stunt to fool fans into thinking they'd get to see the franchise's most iconic character interact with this new cast. Unfortunately for the show's producers, it may not be down to them or the actor, but more corporate concerns.