YES (possibly. Ok, it's a stretch! - answer at the bottom, after I've had my rant)
The logic applied by @Praxis and @N_Soong, is absolutely correct for human beings. There is too much time between the TOS & TNG for a normal human of the next generation to be on TNG.
Mr Spock - he appears in TNG (Season 5, Ep 7&8), so he could easily have had a son, who would be an appropriate age to appear in TNG. I am not aware of Mr Spock having a child.
James T Kirk - was sort-of still alive, inside the Nexus (ST: Generations). No known offspring of "this" Kirk.
Captain Montgomery "Scotty" Scott - trapped in a transporter loop (TNG: Season 6 Episode 4, "Relics"). He was elderly when rescued, so very unlikely to have had children.
Spock's FATHER, Sarek, on the other hand, DOES appear in TNG (so it should be "the previous generation"?!) - Season 5, Ep 7.
Ok, so those are all presumably "no"'s. Who else?
The computer - computer hardware is often referred to is (for example) 5th generation. However, these generations (in 20th century earth) go a lot faster than human generations, so would be unlikely.
This leaves (fanfare please!):
The computer/Majel Barrett-Roddenberry/Lwaxana Troi.
Majel Barrett-Roddenberry portrayed the computer in TOS, and Lwaxana Troi in TNG. Lwaxana's daughter, Deanna Troi, was definitely in TNG.
P.S. - the question has since been edited, specifically eliminating the computer from "bridge crew".