Trapp's career was typical of his times, combining literary and critical activity with religious and political partisanship. He was born into a clerical family in 1679 (his father was rector of Cherrington, Gloucestershire) and after proceeding to New College School, Oxford, and Wadham College, he attracted the attention of the wits by a series of paraphrases, translations, complimentary effusions (including "Peace. A poem: inscribed to ... Viscount Bolingbroke, 1713"), and at least one successful tragedy, _Abra-Mule; or Love and Empire_ (1704). In public affairs he was active in the defence of Henry Sacheverell, and his partisanship here must have cemented his relationship with Dr. William Lancaster, one of the bail for Sacheverell, who was Vice-Chancellor of Oxford at the time of Trapp's election to the chair of poetry. Less fortunate was Trapp's association with the dedicatee of the translation of the _Aeneid_, for Lord North and Grey, who was prominent in seeking to quash Sacheverell's impeachment (and became a privy-councillor in 1711), was committed to the Tower in 1722 for complicity in the Atterbury plot and ended his days a wanderer on the continent. That Atterbury himself was a subscriber to the _Aeneid_ serves further to underline Trapp's Tory affiliations. The dedication by Trapp of his Oxford lectures on poetry (_Praelectiones Poeticae_, 1711-19)[2] to Bolingbroke appears to complete a fatal concatenation of literary and political association in the light of events after the death of Queen Anne.
Nonetheless, Trapp survived and prospered. Under the Tories he had been for a time chaplain to Sir Constantine Phipps, Lord Chancellor of Ireland, and shortly afterwards to Bolingbroke, who stood as godfather to Trapp's son Henry. During the Tory collapse, Peterborough presented him to the rectorship of Dauntsey in Wiltshire; Dr. Lancaster obtained for him the lectureship at St. Martin-in-the-Fields, Westminster; and in the 1730s Bolingbroke, restored, preferred him to the rectorship of Harlington, Middlesex. Other livings and the presidency of Sion College were to accrue for faithful service, as Trapp turned his pen to the defence of the established church: first against the Roman Catholics (for which, perhaps, the University of Oxford created him Doctor of Divinity in 1728) and later against the Methodists, especially in his discourses on _The Nature, Folly, Sin, and Danger of being Righteous over much_ (1739).