The actor (Mark McManus) who played the title role in the UK crime
drama "Taggart" died, but the show still continued under the same name
for quite a few more years. They didn't replace th actor (they of
course had the character die as well), but simply carried on with the
other characters and added new ones over the following years. McManus
died in 1994, but the "Taggart" show carried on until 2010.
The British crime drama "Inspector Morse" finished about two years
before the actor playing the title (John Thaw) role died, but they
basically continued the show by doing a spin-off with his sidekick
"Lewis". When that show in turn was coming to an end, they did have a
set-up for continuing again with another spin-off about Lewis' sidekick
Hathaway, but didn't make it and instead went with the "Endeavour"
prequel one-off about a young detective Morse, which then went on to be
a series which is still going.