Morse and Lewis absolutely.

I'd have to add Morse and Morse from Endeavour. The older detective is always in the background of Russell Lewis's series as his younger self solves cases.

I would add Geordie Keating (played by Robson Green) and whoever else the main priest / detective is (about to be a new one) in Grantchester. Green is one of the most brilliant actors today, and he keeps his character consistent AND fresh throughout the series. Keating is the Sancho Panza to the religious Quixote in these episodes, but in Green's hands he's just as complex as his counterpart.