Gotham has introduced all kinds of legendary characters from DC Comics lore, although almost always with a twist on their origin stories. As Gotham is a new take on Batman plots, it's only natural that fans wonder if the very first Boy Wonder will make an appearance at some point. John Grayson and his future wife Mary both appeared back in Season 1, so Gotham clearly set the stage for Dick Grayson to be born. Now, actor Sean Pertwee (who plays Alfred) has weighed in on whether or not the future Robin 1.0 will appear in Gotham sometime soon, saying this:
She was pregnant when we saw her in the circus episode with Jerome, and presumably that's Robin there in the tummy. We'll see if that comes back around.
John and Mary appeared in "The Blind Fortune Teller" in Season 1. As the episode also happened to feature the introduction of Jerome, their debuts were rather overshadowed, but they ended the episode happily engaged and ready for a life together that definitely wasn't going to end with them both plummeting to their deaths in front of their son. Interestingly, the episode did not reveal that Mary already had a bun in the oven, so either Sean Pertwee knows something that the show didn't give away in Season 1 or he's going with the assumption that baby Robin was going to be born sooner rather than later.
Sean Pertwee spoke about the possibility of Dick Grayson on Gotham during a recent panel at Heroes and Villains Fan Fest in Nashville (via ComicBook.com). His comments at least indicate that there's no reason why Dick couldn't appear on the show, although he could only be a toddler at the very oldest as of Season 4. Unless Gotham suddenly delves into time travel or we get a Gotham: The Next Generation spinoff starring Dick Grayson and Barbara Gordon (who may or may not have been recently conceived), we probably won't get to see Dick Grayson as Robin or Nightwing.
Then again, we do already know that the very last shot of the series is going to be Bruce as Batman, so maybe the show could throw Boy Wonder in as well, even if only as a cameo at the very end. There are definitely ways for Dick to appear on Gotham, so we can only wait and see.
If he doesn't ever turn up on Gotham, there will be other versions of Dick Grayson on the big and small screens in the coming years. Despite all the mentions of Bludhaven on Arrow and The Flash, we probably won't get Dick as Robin or Nightwing on The CW, but the upcoming third season of Young Justice means that we'll have an animated Dick Grayson back on TV. The live-action Titans TV show will star Dick Grayson, and the Nightwing movie in the DCEU will eventually bring him to the big screen.