Generally - unless otherwise stated in the course of a series, the age of a character matches that of the actor playing the role. But with Endeavour Morse, based on the character from the Colin Dexter mystery novels, that poses a bit of a problem.
John Thaw brilliantly played Inspector 'Morse' in the character's first incarnation, totally erasing any memories of his hard-boiled copper in 'The Sweeney' decades earlier. Thaw was born in 1942, but looked older. In the prequel series, Constable 'Endeavour' Morse is played by Shaun Evans who is 33 years old.
But if we take 1942 as the year of birth for Morse because of Thaw, then Endeavour should only be 23 at the time of the prequel. But if Shaun Evans is considered the actor playing his age, then Endeavour is 33 years old. And that would mean Thaw's Morse would be a decade older than the actor playing the role.
We know the series is set in 1965 because of the chronological math presented in the episode "Rocket": Olive Ricks disappeared 12 years before on the day of Queen Elizabeth's Coronation which was June 2, 1953.
(As a side note from a Whovian, on that date the Time Lord known only as The Doctor and his companion Rose Tyler battled an alien known as The Wire.)
So I could have gone either way on this matter. Either Shaun Evans is playing his age and John Thaw was playing ten years older than himself, or vice versa.
However, "Rocket" did also provide another clue - in a conversation with Alice Vexin, Endeavour mentions that it had been about seven years since he left University. And that would at least be closer to the idea of him being born around 1933.
When his mentor Inspector Fred Thursday mentions that Morse would have been too young to have remembered what life was like during WWII when it came to the German scientists now working in England, the idea of Endeavour as a ten year old fits this hypothetical timeline.
The year 1965 as the date for 'Endeavour' had another potential temporal glitch during "Rocket": Even though she was still among the list of suspects, Constable Morse bedded old friend Alice Vexin, who always had a crush on him. The next evening, when he planned to take her to the movies, Morse mentioned to PC Strange that there was a new Bergman movie.... Jim Strange thought he was referring to Ingrid Bergman. The bemused smile on Endeavour's face most likely meant that he was referring to Ingmar Bergman.
But Bergman only made one movie released in 1965, and that was a TV film called "Don Juan". Most likely Morse was referring to "All These Women", which was released in Sweden in June of 1964. It reached the United States by October of that year and Sweden's neighbors still later - December of '64 for Finland and April of '65 for Denmark. (Spain had to wait until 1969 and Portugal finally got it in 1973!)
The IMDb does not give the release date for the British premiere of "All These Women", but it's reasonable to assume that it might have come out late in 1964 or at some point in 1965 and still be considered new by Morse.
Just some more trivial tidbits to enrich your viewing experience!