Dapper Gene Barry moved out of the Old West (Bat Masterson) and into then-modern-day police work on Burke's Law, which bowed on ABC in 1963. I believe the series is simply on hiatus after Me-TV buried the show in late-late-night for the DVR crowd along with its spin-off, Honey West, which we covered a while back.
Police Captain Amos Burke (Barry) might've been the only cop to merit a chauffeur driving him around. Yes, he was rich, so why continue to work? Because someone had to solve the murders among those in the high society circles that Burke traveled.
Unfortunately, some alleged genius at ABC decided that Burke would swap out his badge and become a secret agent in the third season, facilitating a name change to Amos Burke, Secret Agent. Around that same time came Honey West, and by the end of the 1965-6 season, both exited stage left. Reruns of Burke aired locally when I was a lad, and that's how I became acquainted with the series.
Following is the episode, "Who Killed Jason Shaw?", which featured guest stars Keenan Wynn & Burgess Meredith. The Four Star "banner" logo was edited off this video.
And, just for you, here's Amos Burke, Secret Agent:
In 1994, producer Aaron Spelling, who worked on the original series, acquired the rights to the series and brought Amos Burke back to the police force. CBS aired the series as a mid-season replacement in 1994 and 1995. Peter Barton (ex-The Powers of Matthew Star) was cast as Burke's son and partner. Here's "Who Killed The Sweet Smell of Success?", with Robert Culp & Monte Markham:
Edit: 11/10/17: The original video was deleted. Following is a sample clip from the episode, "Who Killed The Sweet Smell of Success?"