In general, comics, series and movies. What's the age difference between Bruce Wayne and Alfred?
In the comics, the answer is "complicated".
In the early comics (the Earth-One and Earth-Two versions) Alfred was roughly the same age as Bruce Wayne: Alfred's father had been Thomas Wayne's butler. He only introduced himself to Bruce after his own father had died and asked Alfred to carry on his legacy as the Wayne's butler. By the time Bruce met Alfred, he was already Batman.
In later comics (starting with the New Earth version), Alfred had been the Wayne's butler for all of Bruce's life, making him most like at least 30 years or so older than Bruce by the time he becomes Batman.
Generally speaking, the movie and television media tend to follow the later comics, where Alfred is already an adult -- and working for the Wayne family -- when Bruce is born. Alfred would be about the same age as Bruce's father, and indeed acts as a surrogate father for the orphan.
We are never given a clear age or birthdate for Alfred, and in the movies, almost nothing is explained about his backstory. In Gotham he's retired from the British military, so he's probably at least in his mid 30s when the series airs (and Bruce is an adolescant).