Except that I wasn’t only referring to his years as a starter for the 49ers. He was the MVP in 1992, yes, but, at that point, he was 31 years old, and in his 8th season in the NFL. He had started for the Bucs for 1 1/2 seasons, and they were so underwhelmed by him that they drafted Vinny Testaverde and traded Young away. When he finally got the chance to start for the 49ers in '91, he was replaced by Steve Bono due to injury, and Bono kept the job (at least briefly) once Young got healthy, because Bono had played well.
Agreed on all points. 
The San Francisco Giants go from Y A Tittle to John Brodie in the 1950s
49ers.
Megastar would be an overstatement, but the Bengals were lucky enough to go from Ken Anderson (who SHOULD be a Hall of Famer) to Boomer Esiaison, who was very good in his own right.
I think Montana to Young is the best you’ll find.
If you’ll wink at a two-year gap, the Dolphins went from Griese to Marino.
Not in the same class, but Jim Hart to Neil Lomax wasn’t bad.
Daryle Lamonica to Ken Stabler is another, although neither had that long a career as starter for the Raiders.
Joe Ferguson to Jim Kelly was a one-year gap.
EDIT: And on rereading, I see astorian already got Lamonica to Stabler.
The Raiders:
Lamonica to Stabler to Plunkett…all Super Bowl QB’s.
My first thought was Montana > Young
My second thought was Staubach > White
Not sure if “megastar” is the right word for George Blanda as a Chicago Bears quarterback but he was on the roster when Sid Luckman’s career was winding down, Although Johnny Lujack was the primary quarterback for two years before Blanda took over. Blanda later had success in the early days of the AFL and then as a place kicker with the Oakland Raiders.
I’ll give some credit because I love Blanda’s later career, but he was a backup QB for nearly all of his career with the Bears. He was only the primary starter in '53, and part of '54 (as you note, Luckman retired after the '50 season), and was mostly a placekicker for the Bears from that point forward.
Not quite what the OP asked but in the late 1950s the Pittsburgh Steelers had a number of great or very good quarterbacks but let them slip away. Keep in mind that while the Steelers have been a well run organization since the early 1970s, they spent their first 40+ years WITHOUT MAKING THE PLAYOFFS ONCE!.
1955 they drafted a kid named Johnny Unitas in the 9th round (Unitas’s school Louisville had de emphasized sports). They cut him after two preseason games without playing hime once and the coach said that Unitas wasn’t very smart. After playing semi pro football he gets a job with Baltimore, becomes a starter with an injury and becomes a Hall of Famer
1957 the Detroit Lions draft on the 17th round a QB named Jack Kemp. That’s Jack Kemp as in 1996 Republican Vice President nominee. They cut him and the Steelers sign him. He plays a little and they and about 4 other NFL teams eventually do the same. He ends up in the new AFL and in the first 6 years with the Chargers and Buffalo (a legendary $100 waiver claim by the Bills) he is the starting QB for five of the first 6 AFL championship games, winning two and named MVP in 1965.
In 1957 the Steelers draft Len Dawson 5th overall (one spot ahead of the Browns who draft Jim Brown). He plays sparingly over 3 years. Hall of Famer with Kansas City in the AFL
Earl Morrall, who was the second player drafted in 1956 by the 49ers is traded to Pittsburgh in 1957. They play him for a year and two games before deciding to get a veteran Bobby Layne. Morrall is most remembered for playing badly in Super Bowl III but he was pretty good. Was twice MVP in 1968 and 1972 replacing injured HOF QBs Unitas and Griese.
Pittsburgh did learn their lesson, sticking with Terry Bradshaw in the 1970s despite some horrible growing pains and giving Kordell Stewart years in the 1990s
Ted Williams to Yaz.
I always felt that Yaz was highly underrated as a quarterback. 
:smack: I meant to mention it’s a baseball comparison.
Red Sox LF succession went from Williams to Yaz to Rice, which wasn’t too shabby. Sure, it wasn’t at quarterback
I agree that Danny White was seriously underrated.
I just went to look up his stats…while I was certainly aware of him when he was playing, I confess that I never really paid a great deal of attention to him (at least in part because I hate the Cowboys 
).
And, I agree, he was pretty good. He had a career completion percentage of 60%, in an era when the West Coast offense was just starting to take hold in the NFL, and 60% was certainly above-average.
Following Staubach surely didn’t help perceptions of him; it likely also didn’t help that he quarterbacked the Cowboys in a period of slow decline, after their strength in the 1970s. He never got the Cowboys to the Super Bowl (losing the NFC Championship Game in each of his first three years as a starter), and didn’t win a playoff game after 1982.
The OP made a mistake…
The Packers went from Bart Star to Brett Favre to Arron Rodgers in succession. 
So, Lynn Dickey and Don Majkowski never existed?