Miguel de Cervantes already had published a few poems in his 20s, but his first novel, La Galatea, was published when he was 38.
At thirty, Albert Schweitzer was an accomplished musician with degrees in philosophy and theology who suddenly decided it was time to go to medical school.
David “Dudu” Fisher was a cantor with no stage experience when he saw Les Miserable in London at the age of 36. He was so mesmerized that he tried out and made his stage debut as Jean Valjean. Later he did the role in Israel and on Broadway.
Kris Kristofferson started acting in his 30s, winning a Best Actor Golden Globe at 40.
Anthony Burgess published A Clockwork Orange when he was 45. He had published a few earlier books, the first one at age 39, but Clockwork Orange was the first big seller.
Oops, never mind! 
Not sure how much this counts as he played on his name. Plenty of sports figures have done the same such as OJ.
Would they have gotten a shot without the name recognition? Not sure it disqualifies them with the OP but throwing it out there.
Would Charles Bukowski count? Not sure if publishing a couple of stories in his 20’s before going on a 10 year drunk before starting to write again really counts? He only started writing full time at age 49…
Faye and Ray Copeland started a new career together when they were 65 and 72. Robert Picton started the same new career when he was 34. All of them were initially farmers before they became mass murderers of considerable repute. Picton was in a class of his own, turning a pig farm and slaughterhouse into a charity party farm and human slaughterhouse.
Jack Iverson was born in 1915. He played cricket as a boy at school (as everybody did) with no success (like nearly everybody) and then became a farm hand, eventually becoming a property manager. He enlisted in the war, and then while mucking about with his mates in the New Guinea jungle, he developed a unique way of bowling. After the war, he thought nothing of it, until someone spotted him helping out with some blind cricketers. He joined the local cricket club in 1947, made it to the Victorian team in 1949, and represented Australia against England in 1950-51 - age 35 - and was probably the key player in the series.
It would be equivalent to someone developing a ‘mystery’ pitch in baseball at age 32, getting to the major leagues at 34 and winning the World Series MVP and Cy Young at 35.
And then he got worked out - he had no real ability other than his ‘mystery’ ball - couldn’t bat, couldn’t field - and basically disappeared.
Jim Morris became a major league baseball player at 35.
Not sure whether to count this, but to err on the side of caution: at thirty, Tim Allen had spent a couple of years behind bars and was holding down a day job while playing stand-up comic in the evenings; if you’d told him he’d soon be an award-winning actor with starring roles in a dozen movies – interspersed with a dozen years of starring roles on television – would he have believed you?
All the writers that have been mentioned started writing after they turned 30? If they get published at 40, but have been writing since they were 13 that doesn’t match the question.
Priscilla Welch started running at age 35 in order to help her quit smoking and get in shape. She ran the 1984 Olympic marathon, finishing 6th, and won the New York City marathon at age 42.
anyone not over the age of 50 and in the UK, would almost certainly have to google her.
She was a honky Tonk sing-a-long Piano player from the 1960’s and released her first album at the age of 43. I imagine she learnt much earlier, so not quite answering the OP question.
Her wider claim to fame was that she recorded at Abbey Road at the same time as the Beatles. She had a special piano made for her which the Beatles used for songs like Ob La Di Bla Da, Lady Madonna plus many others
here’s a lovely picture of the Beatles with it
Abe Vigoda’s work as an actor was mostly as an extra in TV shows until he was 50.
Technically, George Lazenby had never acted in a movie – or on the stage, or on a TV show – before ON HER MAJESTY’S SECRET SERVICE came out after he turned 30.
After working as a street merchant and lounge singer, Jason Statham had no acting experience when he started appearing in movies at thirty-one.
But that doesn’t mean they were “starting their discipline” then. How many of those authors were writing for years before they got published?
The self-taught mathematician George Green.