Technically this is correct. Timothy McGee (Sean Murray) was a recurring character in season 1 before becoming a regular in season 2, and is still with the show.
I don’t think it has happened with the detectives. The closest was probably when Humphrey went to London and worked with Mooney on a case, then Mooney wound up being the new detective after Humphrey went back to London. But some of the junior officers have moved up in rank as senior officers moved on.
It was only a single scene but Emma Peel handing John Steed over to Tara King in The Avengers was about as good as it could get.
How about Blake’s 7? The Blake of the title was the leader of the crew in the first two seasons, but was replaced by crewmember Avon as the leader for seasons 3 and 4.
Similar to the Morse to Lewis example above, if a lot less murdery:
When Andy Griffith decided to leave his namesake sitcom, it was replaced by Mayberry R.F.D., starring Ken Berry as Sam Jones. Sam was head of the town council and, like Andy, a widower bringing up a young son.
The character of Sam was introduced late in the final season of The Andy Griffith Show and became the focus of most of the remaining episodes, and most of the regular Griffith Show cast continued onto Mayberry R.F.D. It was very much a continuation of The Andy Griffith Show with a different lead.
Mayberry R.F.D. isn’t remembered as fondly today as its parent show, but it ran for three seasons and had generally good ratings until it fell victim to CBS’s “rural purge.”
Well sure, if you want to get technical you posted it first, but I bet I thought about it first.
Speaking of lead characters in the title of the show, what about Rosanne? When she was kicked off the show Dan became the lead, but it was always sort of an ensemble cast anyway. Does the name change disqualify it?
BTW, this wouldn’t apply to Valerie → The Hogan Family since Sandy Duncan never appeared alongside Valerie Harper to my knowledge.
ER had a number of leads over the years, even as an ensemble cast. You could certainly make the case that Drs Green and Ross were the original leads, eventually passing off to Carter, and then Kovac.
I was going to say Blake’s Seven.
I think the original Mission Impossible would count as well?
Actually the Avengers works better than that. Steed wasn’t the lead originally- Keel was, but he passed the torch to Steed
It wasn’t my post 
, but I’m sure you thought of it before @TCMF-2L
“Tom Clancy” has now written more books since he died than he ever wrote when he was alive. The franchise of his name keeps them pumping out every six months. One Jack Ryan Jr. novel and one Jack Ryan Sr. novel. And somehow Jack Ryan Sr. is still President of the United States even though his first term started in the 90’s! The new authors also don’t seem to be allowed to kill off legacy characters so Mr. Clark is still in action even though he’s about 80 years old by now. The torch of the franchise was successfully passed but story-wise it’s more of a torch that just stubbornly keeps burning but without any of the light or heat that it used to provide.
Gomer and Goober Pyle of the Andy Griffith show.
I don’t think this was a case of Gomer coming in and Goober eventually leaving on that show, but more a case of Gomer getting his own spin-off series.
Yeah, but they were onscreen together many times.
That’s nice.
So far, that certainly qualifies.
Do non-fiction shows count? What about Ken Jennings appearing as a guest many times on Jeopardy when Alex Trebek was host, then taking over the show when Trebek left?
M, from Judi Dench to Ralph Fiennes
There is Jimmy Palmer working for, then taking over for Ducky on NCIS.
I don’t think she appeared with him in the movies, did she?