He was the son of Thomas Tasker and his wife, Rebecca Isaacs, whose mother was a Sharpe. In 1740, Governor Samuel Ogle was dispatched to England following England's declaration of war against Spain and while he was in England,Tasker was given the governor's power of attorney in Maryland, while he was also the mayor of Annapolis. He was one of the founders of the Baltimore Ironwork Company in 1731. Several newspaper articles documenting his services are available at the Maryland archives including his obituary in “The Maryland Gazzett” dated Jand the sell of his estate in Belle Air in 1771. He was the Annapolis Alderman in 1720 and from 1754 to 1766. He served in the Annapolis municipal government along with provincial government as a member of the President of the Governor's Council from 1722 to 1768 member of the Maryland legislature serving the lower house of the from 1715 to 1722 and the upper house from 1722 to 1766 again in 1768 and President of the Upper House from 1734 to 1766 and acting Governor of Maryland from 1752 to 1753. He was a naval officer until 1742 before entering politics.

He is remembered for serving in many elected and appointed offices, but the most significant in his political career was from 1752 to 1753 as the 21stgovernor of the restored proprietary government of the Colony of Maryland.

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