Clench was the son of John Clench of Wethersfield, Essex and Joan, daughter of John Amias of the same county, and grandson of John Clench of Leeds, Yorkshire. He was admitted a student at Lincoln's Inn on 11 February 1556, called to the bar in 1568, appointed recorder of Ipswich in 1573-1574—being the first known to have held office—elected reader at his inn in Lent 1574, took the degree of serjeant-at-law in Michaelmas term 1580, was appointed a baron of the exchequer in the following year, being assigned to the northern circuit, and on 29 May 1584 was transferred to the court of queen's bench. He was one of the judges appointed to hear causes in chancery in the six months which intervened between the death of the lord chancellor, Sir Christopher Hatton, and the appointment of his successor. He remained, however, attached to the northern circuit, apparently until his retirement. In 1596 he took the Lincoln assizes with Chief-justice Anderson, the bulk of the criminal business consisting, as it would seem, of cases of ecclesiastical recusancy. The unknown writer of a letter preserved in the fourth volume of Strype's Annals says:
'The demeanour of him and the other judge, as they sit by turns upon the gaol in these matters is flat opposite; and they which are maliciously affected, when Mr. Justice Clinch sitteth upon the gaol, do labour to adjourn their complaints to the next assize; and the gentlemen in the several shires are endangered by this means to be cast into a faction'.
Clench is said to have been an especial favourite with Elizabeth. Nevertheless, he does not appear to have been knighted, or in any way honoured. In 1600, while retaining the emoluments of his office, he was displaced from attendance at court, on accountof age and infirmities, and three years later he was pensioned. He died on 19 August 1607, at his seat at Holbrook, and was buried in Holbrook Church, his monument being inscribed as in memory colendissimi suique temporis antiquissimi judicis Johannis Clenche. A half-length portrait of Clench in his robes was long preserved at Harden Hall in Cheshire, but appears to have been among the works of art dispersed in 1815. A portrait of the judge was also in the possession of the town clerk of Ipswich in 1831. Clench was married to Catherine, daughter of Thomas Almot of Creeting All Saints, by whom he had issue five sons and eight daughters. His heir, Thomas, who married Margery, daughter of John Barker, merchant, of Ipswich, was sheriff of Suffolk in 1616, and junior M.P. for the same county in 1630, and one John Clench of Creeting was sheriff of Suffolk in 1630.