A lot of TV shows have had reunion-type made-for-TV movies:
Gilligan’s Island
The Dukes of Hazzard
The Andy Griffith Show
Dallas (?)
Happy Days (?)
Knight Rider (?)
The Sin of Harold Diddlebock (aka Mad Wednesday) shows the life of the hero of The Freshman 20 years later. The last name was changed, but scenes from The Freshman were used, and Harold Lloyd played both roles.
Before Sunset takes place about a decade after Before Sunrise, with the characters catching up on all that’s happened in their lives since they parted.
The first episode of Whatever Happened to the Likely Lads? took place 5 years after the end of The Likely Lads with the same cast.
Absolutely Fabulous took a near-decade long hiatus before coming back for a fourth season. The series pretty much picked up where it left off though - Saffy was still living at home, Patsy still mooching off of Eddie, etc. However the main kitchen set was significantly changed, and there was a running gag about how Eddie had gotten into the habit of obsessively redecorating the kitchen over and over again.
The Britcom Are You Being Served?, set in the Grace Bros. Department Store, was followed years later by Grace & Favour (AKA Are You Being Served? Again!, in which the majority of the cast had retired together to run a hotel in the English countryside.
It was but a shadow of its former self.
There was also Michael Apted’s series of documentaries: Seven Up, Seven plus Seven, 21, 28 Up, 35 Up, 42 Up. and 49 Up, which follow the same group of children from age 7 to age 49 to see their lives unfold.
Some of the movies, such as the Star Trek movies and Gilligan’s Island made-for-TV movies, that I thought of have been mentioned.
I seem to remember a Flintstones sequel with a teenage Pebbles and Bam-Bam.
No new episodes have been greenlit.
In any case, ST:TMP does fit the criteria of the OP (original cast several years later: Kirk is an admiral, Spock and McCoy are out of the service, etc as the stage is set).
There was a one-shot special in 1997:
in which the pretense was that the series The Monkees had been running for thirty years. The characters were all back. They were supposed to be living in the same house as in the series. The characters talked as if the series had kept running for those thirty years and would make mention of episodes from those imaginary years as if they really existed.
Rugrats had a follow-up series, All Grown Up, in which all the characters were 10 years older, and it included characters introduced in the movie Rugrats in Paris.
CHiPs '99
Perry Mason was revived with the (surviving) original cast in the 80s for a series of TV movies.
Also The New Leave it to Beaver.
“Eight is Enough” had some TV movies with the children having families of their own.
There was a short-lived new series of Mission Impossible with Peter Graves as an older Phelps leading a new team of agents (including one who was supposed to be the son of a character from the original series).
We’ll pretend the movies don’t exist though.
There was the Facts of Life Reunion movie with Lisa Welchel, Mindy Cohn and Kim Fields, but no Nancy McKeon. Natalie is fending off marriage proposals, Blaire runs a hotel empire and Tootie is trying for a talk show.
Patrick MacNee returned as John Steed in The New Avengers. Nobody else came back, though. I understand Diana Rigg made a guest appearance in one episode, but I must have blinked – I missed her.
National Velvet
1944
Elizabeth Taylor as the 12-yr-old Velvet Brown.
International Velvet
1978
Nanette Newman as the 46-yr-old Velvet Brown.