Out of interest I looked at the New York Times archive. You only can read the whole articles if you pay, but the headlines are enough
June 15, 1963
Prince Will Attend Stanford
Prince Will Attend Stanford - Article - NYTimes.com
November 29, 1963
British Prince Is Arrested On Coast Traffic Charge
Prince William was cited by a last night for sports car across the in the Los Altos hills.
British Prince Is Arrested On Coast Traffic Charge - Article - NYTimes.com
December 17, 1963
British Prince Gets an 'A' for Work at Stanford; But Elizabeth's Cousin Plans to Stop Seeking Master's He Wants to Chart Career in Commonwealth Relations
British Prince Gets an 'A' for Work at Stanford - But Elizabeth's Cousin Plans to Stop Seeking Master's He Wants to Chart Career in Commonwealth Relations - Article - NYTimes.com
February 25, 1964
Prince Fails Test For British Post On Second Attempt oops
Prince William of Gloucester, one of Queen Elizabeth's fa*vorite cousins, has failed a Civil Service entrance examination for the second and last time, it was announced today.
The 22‐year‐old Prince is tak*ing a post‐graduate course in economics at Stanford Univer*sity in California.
A family spokesman said Prince William had been in*formed that he had failed the examination for entry into the Commonwealth Relations Of*fice.
“This is the second time he has taken the examination, the first being when he was at Cambridge, and unluckily he has just failed each time,” the spokesman said.
“Unfortunately, under the regulations he cannot have an*other go.”
“Prince William is naturally very disappointed,” the spokes*man added. “He had hoped that he might be able to do a useful job in this field.”
The Prince completes his year at Stanford this summer. He is expected to spend the Easter vacation at home in Britain.
“Obviously he will be discus*sing his future with his parents,” the spokesman said.
The Prince's father, the Duke of Gloucester, who is the third son of King George V, had planned a military career for his son. But the Prince chose otherwise.
http://www.nytimes.com/1964/02/25/prince-fails-test-for-british-post-on-second-attempt.html
January 05, 1965
British Prince Takes Job LONDON, Jan. 4 (UPI) -- Prince William of Gloucester, 23-year-old cousin of Queen Elizabeth II, began today a $42a-week job as an apprentice in the
British Prince Takes Job - Article - NYTimes.com
October 05, 1965
Prince Begins Training LONDON, Oct. 4 (UPI) -- Prince William of Gloucester, a cousin of Queen Elizabeth II, started a .month s training today for his much- past as a diplomat.
July 17, 1970
LONDON, July 16 (AP) Prince William of Gloucester, the 28-year-old first cousin of Queen Elizabeth II, has resigned from the diplomatic service, the Foreign Office announced today.
British Prince Quits as Diplomat - Article - NYTimes.com