Princess Alice, wife of Henry, Duke of Gloucester, was King George V's daughter in law and aunt to Queen Elisabeth II.
In February 1945, she and her husband were honored by three stamps of Australia, where he was becoming Governor-General, representing the King in the place. Their uniforms reminded that the time of war was still on.
Another Princess Alice, the daughter of Queen Victoria's younger son, was honored by one of the stamps issued by Trinidad and Tobago this 3 October 2008 for the sixtieth anniversary of the University of the West Indies, whose she was the first chancellor. But, it was not the first stamp of her long life (1883-1981).
In 1951, the States participating to the creation of the University of the West Indies launched a omnibus two-stamp issue: the arms of the university on the first, the new chancellor on the second. Certainly, the English-speaking Caribbean post offices may have issue stamps in her honor since the fifties (but I lack catalogs).
During a Google search, I found two text cancellations of Jamaica around 1955 (1 et 2), visibly a call to donate to a charity leaded by Princess Alice because the first years of the university were financially difficult.
Thank to the Stanley Gibbons' Commonwealth & British Empire Stamps 1840-1970 catalog, very useful: British world only, stamp designers and printers quoted, precise dates of issues, etc.