His connections with Clare College at Cambridge allowed Paske to greatly influence the election of Charles I's favorite, George Villiers, Duke of Buckingham to the Chancellorship of his alma mater in 1626.
The election created national controversy as Buckingham was under articles of impeachment by Parliament for corruption and embezzlement of treasury funds.
He took up his residence at Canterbury, and the fellows of Clare consequently petitioned for and obtained from Charles I, some time before 2 September 1640, permission to elect a successor; but no appointment was made until 1645, when Ralph Cudworth was put in by Parliament.
Paske was also subdean of Canterbury, and on 30 August 1642 complained to Henry, Earl of Holland, of the ruthless treatment of the cathedral by troopers of Colonel Edwin Sandys's regiment.
Paske, after being deprived of all his benefices, at the Restoration was reinstated in the rectory of Hadham, in his two prebends, and in the mastership of Clare Hall; but he surrendered his right of restitution to the latter in favour of his son-in-law, Theophilus Dillingham who succeeded Ralph Cudworth in 1664.