The son of Major Edward Abbott, a civil official in the colony of Van Diemen's Land, Edward Abbott was appointed clerk to his father in 1818. He became a pastoralist, and his claim to the ownership of certain land near Launceston became the subject of a long running dispute between Abbott and the colonial and British governments. In 1848 he became a police magistrate, and he was later elected as a Tasmanian MP.
Abbott was the editor, publisher and original proprietor of the Hobart Town Advertiser, which he began in April 1839 - and which strongly supported the government of Sir John Franklin. Although Abbott sold the Advertiser in 1842, he seems to have been retained as publisher and probably as editor for a time. In 1844 he became embroiled in a bitter personal dispute with another Tasmanian newspaper editor (Robert Lathrop Murray), which eventually led to the new owners of the Advertiser being sued for libel.