I agree totally. And yet, Mulgrew herself was a replacement.
I’ll go out on a limb here to say I think Bonanza actually improved after Pernell Roberts left the cast. The writers still had Ben for the serious story lines, but had room to expand the Hoss and Little Joe characters and could play with lighter, more comedic plots.
Barney Miller was supposed to focus more or less equally on Barney’s home and work life. It turned out that the work setting was far better and Barney’s wife Elizabeth (Barbara Barrie) was written out of the show.
I don’t know that Charlies Angels got “better” but the loss of Farrah Fawcett and Kate Jackson didn’t seem to hurt the show badly.
The departure of Kes and the addition of 7 of 9 improved Voyager.
And what exactly is wrong with that?
There’s only room in our hearts for one shew and you’ve already taken that spot.
Marc
NYPD Blue benefited by the departure of David Caruso. Caruso wasn’t much to start with and by getting rid of him it created the opening to develop Dennis Franz’ character.
The big mistake was not replacing Radar with a new character.
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Elisabeth Rohm on Angel. She served very little purpose and was distracting.
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McLean Stevenson from MASH. I like Wayne Rogers a lot too, but Col. Potter(Harry Morgan) really lifted the shows quality a lot.
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Shelly Long from Cheers. The show was way better after Diane was out of the picture.
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Michael O’Hare from Babylon 5. It was the right choice by both O’Hare and JMS to move on without him. Bruce Boxleitner, while not a great actor, had a better written character and he’s a better TV actor(O’Hare is a stage actor).
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David Duchovny from X-files
Kidding! 
They did drop Klinger into the slot . . . but it just wasn’t the same . . .
Oz kept getting better and better… and lost major stars like, ALL the time 
I’ve wondered before if the producers decided that Klinger’s drag act was getting old or if Jamie Farr brought it up when his contract was up for renewal, because that’s about the same time he started wearing fatigues only.
Until this post I actually assumed Patrick McNee was always the star. I’m probably not alone- Hendry’s episodes must not have been that memorable. (McNee’s autobio, Blind in One Ear, is one of the most best celebrity memoirs ever, incidentally, especially his childhood (among other unusual moments was when his mother left his dad for a butch lesbian coal mine heiress and farmer he called “Uncle Evelyn” who required McNee and his brother to wear dresses when they visited).
While I was never a fan of Saved by the Bell (I’m about 15 years or so too old for their target audience) IIRC it began as a sitcom starring Halley Mills, who left after the first season. I could imdb it, but I don’t believe it was called Saved by the Bell in the Mills episodes, but obviously she’s forgotten and the show became a huge success.
Farrah was dispensable, but no one could replace Kate.
Oh yeah, they called it “Good Morning, Miss Bliss,” and the focus was pretty much on her/the teachers’ perspective. Then after she left, the style where Zach Morris would narrate and use his ultra huge cell phone was introduced. I knew all that, but until now, I had no idea that Haley Mills of the Parent Trap was Miss Bliss. Gosh.
I don’t have the hate for The Wesley that other people seem to have. I’ll admit I liked it more when he went off to Starfleet Academy. It made him seem more adult-like. Of course that necessitated him leaving the Enterprise, so he was a lot less of a regular character by then. But it made him seem more of a legitimate part of the crew when he returned during the episodes that placed him on leave.
This would have been mine if I’d gotten here first. That 1st season was painful, and if there weren’t a number of foundation-laying episodes in it, I would suggest that newbies to the series just start with season 2.
I’ve said before that they could have replaced O’Hare with a hockey stick and gotten a less wooden performance.
Way late to the party, but MAS*H and **NYPD Blue ** saw big improvements with early Stars leaving.
**Nightcourt ** changed casts several time and greatly improved by Paula Kelly & Ellen Foley being replaced by Markie Post as Christine Sullivan. Loosing Selma Diamond hurt the show, but later when Florence Halop also past away, Marsha Warfield was a big improvement.
Carl Reiner replacing himself and the entire cast of “Head of the Family” (1960) where he play Rob Petrie was a decision that made TV history. This show of course became the Dick Van Dyke show with Mary Tyler Moore, Morey Amsterdam & Rose Marie starring and Carl becoming the Sid Caesar like star of the show within the show.
**Taxi ** quickly replace the quirky young character John Burns (Randall Carver) with Reverend Jim and became the best show on TV for about 3 years.
Nitpick: John Burns was a minor recurring character (granted, he seems to have been intended to be one of the leads, but he just never got the screen time to qualify) throughout the first season, and Reverend Jim did appear during the first season and then become a regular in season two, but IMHO saying Jim replaced John is overstating it just a bit. It’s like saying Geordi “replaced” the string of losers that had the job of Chief Engineer on TNG’s first season. In Reverend Jim’s case, they had a character they loved and found a place to put him.
Maybe not exactly the kind of thing the OP was loking for, but The Daily Show got better when Jon Stewart replaced Craig Kilborn. The show wasn’t bad with Kilborn, but Stewart took it to a whole different level.
It is a fair nitpick, but John was originally to be a major character. Several early shows dealt with him and his new wife minimizing everyone elses role except Alex.
That is a great example. The old Kilborn show was pretty blah, the new Jon Stewart version has been sustained greatness.
In Britcoms, Men Behaving Badly took off after Harry Enfield’s departure.
The Daily Show is better with John Stewart than Craig Kilborn. Even though I liked Craig Kilborn.