Question: Which daughter of the King of the United Kingdom of Great Britain and Ireland and King of Hanover from 26 June 1830 until his death was an infant member of the British royal family?

Context articles: Princess Caroline of Gloucester
Prince George William of Great Britain
Georgian architecture
Monarchy of Ireland
William IV of the United Kingdom
George III of the United Kingdom
British Royal Train
George IV of the United Kingdom
Governance of England
Princess Elizabeth of Clarence

Princess Caroline of Gloucester (Caroline Augusta Maria; 24 June 177414 March 1775) was an infant member of the British Royal Family, a great-grandchild of George II, niece of George III and daughter of the 1st Duke of Gloucester and Edinburgh and his wife, Maria Walpole, daughter of Sir Edward Walpole and his mistress Dorothy Clement.
Prince George William of Great Britain (13 November 1717 – 17 February 1718) was an infant member of the British royal family, second son of George II and Caroline of Ansbach who, at the time of his birth, were the Prince and Princess of Wales.
 He died aged 3 months, 4 days.
Georgian architecture is the name given in most English-speaking countries to the set of architectural styles current between 1714 and 1830.
 It is eponymous for the first four British monarchs of the House of Hanover—George I, George II, George III, and George IV—who reigned in continuous succession from August 1714 to June 1830.
 The style was revived in the late 19th century in the United States as Colonial Revival architecture and in the early 20th century in Great Britain as Neo-Georgian architecture; in both it is also called Georgian Revival architecture.
 In the United States the term "Georgian" is generally used to describe all buildings from the period, regardless of style; in Britain it is generally restricted to buildings that are "architectural in intention", and have stylistic characteristics that are typical of the period, though that covers a wide range.
A monarchical system of government existed in Ireland from ancient times until, for what became the Republic of Ireland, the mid-twentieth century.
 Northern Ireland, as part of the United Kingdom, remains under a monarchical system of government.
 The Gaelic kingdoms of Ireland ended with the Norman invasion of Ireland, when the kingdom became a fief of the Holy See under the Lordship of the King of England.
 This lasted until the Parliament of Ireland conferred the crown of Ireland upon King Henry VIII of England during the English Reformation.
 The monarch of England held the crowns of England and Ireland in a personal union.
 The Union of the Crowns in 1603 expanded the personal union to include Scotland.
 The personal union between England and Scotland became a political union with the enactments of the Acts of Union 1707, which created the Kingdom of Great Britain.
 The crowns of Great Britain and Ireland remained in personal union until it was ended by the Acts of Union 1800, which united Ireland and Great Britain into the United Kingdom of Great Britain and Ireland from January 1801 until December 1922.
William IV (William Henry; 21 August 1765 – 20 June 1837) was King of the United Kingdom of Great Britain and Ireland and King of Hanover from 26 June 1830 until his death.
 The third son of George III and younger brother and successor to George IV, he was the last king and penultimate monarch of Britain's House of Hanover.
George III (George William Frederick; 4 June 1738 – 29 January 1820) was King of Great Britain and Ireland from 25 October 1760 until the union of the two countries on 1 January 1801, after which he was King of the United Kingdom of Great Britain and Ireland until his death.
 He was concurrently Duke and prince-elector of Brunswick-Lüneburg ("Hanover") in the Holy Roman Empire until his promotion to King of Hanover on 12 October 1814.
 He was the third British monarch of the House of Hanover, but unlike his two predecessors, he was born in Britain, spoke English as his first language, and never visited Hanover.
In the United Kingdom, the Royal Train is used to convey senior members of the British Royal Family and associated staff of the Royal Household around the railway network of Great Britain.
 It is formed from a dedicated set of claret liveried sleeper, dining and lounge carriages.
 The current stock dates from 1977-1987.
 They are arranged according to requirements, and stored when not in use.
 The earliest royal coaches date back to the mid-19th Century in the reign of Queen Victoria; until an upgrade in 1977 there were multiple sets based in different regions, a legacy of the pre-nationalisation era of railways in Britain.
 Many are now in museums or on heritage railways; the National Railway Museum in York has a royal themed exhibition.
 Dedicated locomotives have never traditionally been part of the Royal Train, first appearing in special livery only in the 1990s, but also seeing use on other trains since 2003.
 In the 21st Century, various preserved (and one new build) steam locomotives have also hauled the train on special occasions.
 Although regularly cited by critics as one of the unnecessary luxuries of the Royal Family, which has led to an increase in the alternate use of normal scheduled services where possible, supporters argue the current arrangement emphasizes utility over luxury, and is still often the most practical and secure mode of travel to fit the required itinerary and avoid disruption to the public.
George IV (George Augustus Frederick; 12 August 1762 – 26 June 1830) was King of the United Kingdom of Great Britain and Ireland and of Hanover following the death of his father, George III, on 29 January 1820, until his own death ten years later.
 From 1811 until his accession, he served as Prince Regent during his father's final mental illness.
There has not been a government of England since 1707 when the Kingdom of England ceased to exist as a sovereign state, as it merged with the Kingdom of Scotland to form the Kingdom of Great Britain.
 Kingdom of Great Britain continued from 1707 until 1801 when it merged with the Kingdom of Ireland to form the United Kingdom of Great Britain and Ireland, which itself became the United Kingdom of Great Britain and Northern Ireland (UK) in 1922 (in reality; in name in 1927) upon independence for most of the island of Ireland.
 The UK since then has gone through significant change to its system of government, with devolved parliaments, assemblies and governments in Scotland, Wales and Northern Ireland.
 England, however, remains under the full jurisdiction, on all matters, of the Parliament of the United Kingdom of Great Britain and Northern Ireland and the UK government as no devolved administration has been created for England within the new structure.
 This situation has led to the anomaly, known as the West Lothian question, which is that Scottish Members of Parliament (MPs) are able to vote on legislation that affects only England whereas English MPs can not vote on certain Scottish matters due to devolution.
 In some cases, such as top-up university tuition fees and foundation hospitals, the votes of Scottish MPs have been crucial in helping pass legislation for England that the majority of English MPs have opposed.
Princess Elizabeth of Clarence (Elizabeth Georgiana Adelaide; 10 December 1820 – 4 March 1821) was an infant member of the British royal family.
 She was the second daughter and third child of Prince William, Duke of Clarence and St Andrews (later King William IV) and his wife (later Queen), Princess Adelaide of Saxe-Meiningen.
 She was a granddaughter of King George III of the United Kingdom and a first cousin of Queen Victoria.