Elton was a merchant and industrialist, and like his father before him, he served as the High Sheriff of Bristol from 1710–11. He invested in slave ships with his brothers, Isaac and Jacob. He was the Master of the Society of Merchant Venturers in 1719 and Mayor of Bristol from 1719–20, but in 1720, he was made bankrupt during the "South Sea Bubble". As soon as he completed his term as Mayor, he left Bristol and travelled to France, and did not return until his father paid off his debts.
Elton returned to England by 1724, and stood in the Taunton by-election of 1724 for the Whigs, as an unexpected late entrant. He was duly elected to serve as a Member of Parliament for Taunton, though one of the other candidates, George Deane, filed a petition against his election. The petition was rejected by a vote of 151 to 104. He only served Taunton until the general election, in 1727, when his father vacated his seat in Bristol. At the resulting election, Elton paid his Tory opponent £1,000 to withdraw from the election, allowing him to be returned unopposed. In Parliament, he became a member of the gaols committee. Upon his father's death on 9 February 1728, Elton became Sir Abraham Elton, 2nd Baronet, and inherited Clevedon Court. In February 1730 he spoke against the Royal African Company’s petition to be spared the cost of maintaining their forts. He often petitioned government on mercantile issues, amongst them; in 1730 for the removal of duty on soaps and candles, five separate times for the removal of duty on Irish yarn, twice against the introduction of slave duties. He was said to have made a "bantering speech" against the proposed Excise Bill of 1733. Elton topped the poll in a contest at the 1734 British general election. He continued raising petitions on mercantile issues, and voted with the Opposition in all recorded divisions. He was returned unopposed at the 1741 British general election.
Death
Elton died on 20 October 1742, leaving three sons and three daughters. The baronetage passed to his eldest son, who became Sir Abraham Elton, 3rd Baronet but died without issue. The baronetcy then passed to his brother Sir Isaac Elton, 4th Baronet. Another of Elton's sons, Jacob became a Royal Navy captain but was killed in a sea battle. Elton's daughters Mary and Elizabeth married.