Question: What years did ponsonby baronet serve a conservative politician before they became a prime minister

Context paragraphs:
Han Myeong-sook: Han Myeong-sook (born March 24, 1944; Korean: 한명숙 ] ) was the Prime Minister of South Korea from April 2006 to March 2007.  She is South Korea's first female prime minister (second female prime minister overall if the acting premiership of Chang Sang is included).  She was from the United New Democratic Party (UNDP) as a member of the Korean National Assembly (representative) for Ilsan-gab, and is a graduate of Ewha Womans University in Seoul with a degree in French literature.  She resigned as Prime Minister on March 7, 2007 and declared her presidential candidacy.  But she did not succeed in the nominations.  In 2008 she ran for parliament, but was not elected.  However, in January 2012 she was elected leader of the main oppositional Democratic United Party (DUP) before the April legislative elections and became a member of parliament.  But the liberals did not manage to defeat the ruling Saenuri Party and Han stepped down as party leader in April 2012.  In August 2015, Han was convicted of receiving illegal donations at the amount of 900 million KRW, and sentence to two years in prison.  She is ineligible to run for public office for ten years after her prison term.  She became the first former prime minister of the Republic of Korea to serve a prison time.

Anthony Eden: Robert Anthony Eden, 1st Earl of Avon, (12 June 1897 – 14 January 1977) was a British Conservative politician who served three periods as Foreign Secretary and then a relatively brief term as Prime Minister of the United Kingdom from 1955 to 1957.

Heathcoat-Amory baronets: The Heathcoat-Amory Baronetcy, of Knightshayes Court in Tiverton in the County of Devon, is a title in the Baronetage of the United Kingdom.  It was created for John Heathcoat-Amory on 21 March 1874.  The businessman and Liberal politician was born John Amory, and was the maternal grandson of John Heathcoat and assumed by Royal licence the additional surname of Amory.  The title descended from father to son until the death of his grandson, the third Baronet, in 1972.  He was succeeded by his younger brother, the fourth Baronet.  He was a Conservative politician.  In 1960, twelve years before he succeeded in the baronetcy, he was raised to the Peerage of the United Kingdom as Viscount Amory, of Tiverton in the County of Devon.  Lord Amory was unmarried and on his death in 1981 the viscountcy became extinct.  He was succeeded in the baronetcy by his younger brother, William, the fifth Baronet.  As of 2007 the title is held by the latter's eldest son, the sixth Baronet, who succeeded in 1982.

Sir William Mount, 1st Baronet: Sir William Arthur Mount, 1st Baronet CBE (Hartley, Hampshire, 3 August 1866 – 8 December 1930) was a British Conservative Party politician and Member of Parliament for the Newbury constituency.  He is the great-grandfather of Conservative politician David Cameron, who was Prime Minister of the United Kingdom from 2010 to 2016.

Ömürbek Babanov: Ömürbek Toktogulovich Babanov (Kyrgyz: Өмүрбек Токтогулович Бабанов; born 15 January 1970) is a Kyrgyz politician who was Prime Minister of Kyrgyzstan from 1 December 2011 to 1 September 2012.  Before his appointment as Prime Minister, he was Deputy Prime Minister in the Government of Almazbek Atambayev.  He was also acting Prime Minister from 23 September 2011 until 14 November 2011, as the Prime Minister Atambayev was a candidate in the presidential election.  He again became acting Prime Minister on 1 December 2011 when Atambayev took office as President.  He was confirmed by Parliament on 23 December 2011.  On 1 September 2012 Babanov resigned as Prime Minister.

Baron Belstead: Baron Belstead, of Ipswich in the County of Suffolk, was a title in the Peerage of the United Kingdom.  It was created on 27 January 1938 for the Conservative politician Sir John Ganzoni, 1st Baronet.  He had already been created a Baronet, of Ipswich in the County of Suffolk, in the Baronetage of the United Kingdom on 22 March 1929.  He was succeeded by his son John, the second Baron.  He was also a Conservative politician and served as Leader of the House of Lords from 1988 to 1990.  After the passing of the House of Lords Act 1999, Lord Belstead was created a life peer as Baron Ganzoni, of Ipswich in the County of Suffolk, on 17 November 1999, in order to allow him to remain in the House of Lords.  He never married and the titles became extinct on his death in 2005.

Sir Richard Glyn, 9th Baronet: Lieutenant-Colonel Sir Richard Hamilton Glyn, 9th Baronet OBE, TD, DL (12 October 1907 – 24 October 1980) was a British army officer, Conservative politician and authority on breeding pedigree dogs.  He was the son of Sir Richard Glyn, 8th Baronet, and his wife Edith Hamilton-Gordon, the great-granddaughter of the Prime Minister Lord Aberdeen.

Ponsonby baronets: The Ponsonby Baronetcy, of Wootton in the County of Oxford, is a title in the Baronetage of the United Kingdom.  It was created on 27 January 1956 for the Conservative politician Charles Ponsonby.  He had earlier represented Sevenoaks in the House of Commons and served as Parliamentary Private Secretary to the Foreign Secretary Anthony Eden from 1941 to 1945.  A member of the prominent Ponsonby family headed by the Earl of Bessborough, he was the son of the Hon. Edwin Charles William Ponsonby, fourth son of Charles Ponsonby, 2nd Baron de Mauley.  As of 2010 the title is held by the second Baronet's son, the third Baronet, who succeeded in 2010.  His father was Lord Lieutenant of Oxfordshire between 1980 and 1996.  As a descendant of the second Baron de Mauley, he is also in remainder to this title as well as to the earldom of Bessborough.

Viscount Brentford: Viscount Brentford, of Newick in the County of Sussex, is a title in the Peerage of the United Kingdom.  It was created in 1929 for the Conservative politician Sir William Joynson-Hicks, 1st Baronet, chiefly remembered for his tenure as Home Secretary from 1924 to 1929.  He had already been created a baronet, of Holmsbury, in the Baronetage of the United Kingdom, on 20 September 1919.  His younger son, the third Viscount, was also a Conservative politician.  On 29 January 1956, two years before he succeeded his elder brother in the viscountcy, he was created a baronet, of Newick.  s of 2017 the titles are held by the third Viscount's son, the fourth Viscount, who succeeded in 1983, a retired solicitor and has served as the president of the Church Society.

Dalrymple-Hay baronets: The Dalrymple-Hay Baronetcy, of Park Place in the County of Wigtown, is a title in the Baronetage of Great Britain.  It was created on 27 April 1798 for Colonel John Dalrymple-Hay.  Born John Dalrymple, he was the husband of Susan, daughter of Sir Thomas Hay, 3rd Baronet, of Park (see Hay baronets for earlier history of this title).  On inheriting his father-in-law's estates in 1794 he assumed by Royal licence the additional surname of Hay.  Four years later the baronetcy held by his father-in-law was revived in his favour.  His grandson, the third Baronet (who succeeded his father), was an Admiral in the Royal Navy and Conservative politician.  His third and youngest son, the fifth Baronet (who succeeded his childless elder brother), was a Clerk in the Foreign Office from 1887 to 1895 and in the Privy Council Office from 1895 to 1928.  On his death the line of the third Baronet failed and the title passed to the late Baronet's first cousin twice removed, the sixth Baronet.  He was the eldest son of Brian George Rowland Dalrymple-Hay (1898–1943), a Colonel in the Indian Cavalry, son of George Houston Dalrymple-Hay (1865–1948), fifth son of George James Dalrymple-Hay (1828–1891), a Colonel in the Bengal Staff Corps, second son of the second Baronet (and eldest son of his second marriage).  As of 2009 the title is held by the seventh Baronet's son, the eighth Baronet, who succeeded in January 2009.

Supporting paragraphs: Ponsonby baronets Anthony Eden
Answer: Prime Minister of the United Kingdom from 1955 to 1957