He was the third son of Sir Edward Astley, 4th Baronet of Melton Constable and Rhoda Delaval, daughter of Francis Blake Delaval of Seaton Delaval, Northumberland. He attended Westminster School and Trinity College, Cambridge. On 14 January 1789 he married Hester Browne, by whom he had three sons and six daughters. His father Edward was MP for Norfolk for twenty-two years and gave it up in 1790 rather than contest it. Jacob was given a commission as a captain in the East Norfolk Militia in 1780, which he held until 1794, when he was made lieutenant colonel in the Norfolk Fencible Cavalry, a role he held for five years. He was on military service in Scotland in 1797 when his mother announced his candidature for one of the seats in his father's old constituency, which had fallen vacant when Sir John Wodehouse was made a peer. The constituency's other MP Thomas William Coke offered him financial help and Astley was returned unopposed, despite Wodehouse threatening to refuse his peerage and remain MP to block his election. Astley professed neutrality and publicly distanced himself from Coke, but he did vote with the Whigs against William Pitt the Younger's assessed taxes and land tax redemption in late 1797 and early 1798, against the refusal to enter into peace negotiations with France in 1800 and for the censure motion by Grey on 25 March 1801. By his father's death in 1802 both his elder brothers had died and so he inherited the baronetcy and Melton Constable Hall in Norfolk. Again assisted by Coke, his re-election campaign of 1802 was fierce and he was attacked as "a liar, a coward, an assassin, a scoundrel, a murderer; and... his own father". He initiated a libel case, though the defence cited his own father's words just before his death and Astley was only awarded a fifth of the £10,000 damages he claimed. When his mother's brother Edward Hussey Delaval died in 1814 he inherited his estate of Seaton Delaval Hall in Northumberland. The 1806 election elected Coke and William Windham as the MPs for Norfolk, but on petition this result was declared invalid and in a by-election the following year Coke's younger brother Edward and Astley were elected instead. Astley took leaves of absence in 1815 and 1816 and died in 1817. His eldest son Jacob succeeded him in the baronetcy.
