Clements, Henry Theophilus (1734–95), financial administrator and MP, was second son of Nathaniel Clements (qv), treasury official and MP, and his wife Hannah, daughter of the Rev. William Gore, dean of Down. The younger brother of Robert Clements (1732–1804), 1st earl of Leitrim, he resided at Ashfield Lodge, Cootehill, Co. Cavan, and at Woodville, Lucan, Co. Dublin. He was commissioned in the 30th Regiment of Foot (1757) and rose to become lieutenant-colonel of the 69th Regiment (1764–5). In 1772 he succeeded his father as agent to regiments serving abroad (£800 a year) and on his death in 1777 became deputy vice-treasurer and paymaster of pensions (each position worth about £1,200 a year). Although not the eldest son, he inherited his father's estate at Ashfield Lodge (with a rental of almost £3,000 a year). He was also a trustee of the Irish linen board (1779–95), and high sheriff of Co. Cavan (1766) and Co. Leitrim (1773). Patron and MP for Cavan borough (1769–76, 1783–90) and MP for Co. Leitrim (1776–83, 1790–95), he was a staunch government supporter, voting against legislative independence and parliamentary reform, but for catholic relief (1774, 1778). Unseated on petition in Co. Leitrim in 1783 for bribing voters, he fell back on his seat for Cavan. He was colonel of the Leitrim Rangers Volunteers in the early 1780s and was Co. Cavan delegate to the Volunteer National Convention of 1783; he later became colonel of the Co. Leitrim militia (1793–5).
Marrying into the Beresfords in 1778, he commanded lucrative revenue patronage, and on 25 December 1783 was appointed paymaster and receiver general of Ireland, which replaced the office of deputy vice-treasurer, and was appointed to the privy council. In 1785 it was estimated that he held government positions worth £2,400 a year. He was a member of the committee that prepared the draft bill for the establishment of the Bank of Ireland, and he subscribed the maximum permissible sum of £10,000 to the bank's capital on its foundation in 1783. A skilled and innovative financier, he sought to reform the entire system of financial administration in Ireland by extending the bank's services to all departments of state, including the revenue commissioners, and instituting a policy of repaying the Irish national debt by issuing treasury bills. He was also closely involved in the development of a very successful national lottery (1786–7) to reduce interest charges on the national debt. He acted as the Dublin agent of the Cork banking house of Falkiner, Rogers, Leslie, & Kellett, and handled large sums of money for the army in Ireland. Although he did not discount bills, in effect he ran a private banking operation in the early 1780s. He died 26 October 1795 at his home in Co. Leitrim and was buried in St Michan's church, Dublin. He was succeeded by his eldest son, Henry John Clements (1781–1843), MP for Co. Leitrim (1805–18) and Co. Cavan (1840–43).
He married first (2 June 1770) Mary (d. 1777), daughter and heiress of Gen. Daniel Webb, with whom he had two daughters; and secondly (7 August 1778) Catherine, eldest daughter of John Beresford (qv), commissioner of revenue; they had three sons and two daughters.