J.A.R.V.I.S. is the AI built by Tony Stark as an aid & house-help (Butler) based on Jarvis who was the aid & house-help (Butler) of Howard Stark, Tony's father.
J.A.R.V.I.S. is voiced by Paul Bettany & Jarvis is played by James D'Arcy.
Iron Man came out first & then a few years later, Agent Carter came out.
So the question can be either why Paul Bettany, who voiced J.A.R.V.I.S., didn't play Jarvis in Agent Carter or why James D'Arcy didn't voice J.A.R.V.I.S. in Iron Man & subsequent films.
Their (Jarvis's) mannerisms are very similar so from a sense of continuity why didn't MCU producers hire the same actor to play both roles. A word from producers would be great.