Price was the son of Rees ap Tudor and his wife Margory, who was the daughter of Edward Stanley (constable of Harlech Castle).
In 1604, he was appointed as Principal of Hart Hall, Oxford (the predecessor of Hertford College), holding this position until his resignation in 1622.
He was one of two clerics chosen in 1622 to serve on a commission sent to Ireland to explore grievances, including investigation of the state of the church.
[1] Price died at Westminster on 15 December 1631 in circumstances that confirmed to some contemporaries the close link between Laudian ceremonials and Roman Catholicism.
The Philip Herbert, 4th Earl of Pembroke was reported to have remarked to King Charles I, "Is this the Orthodox man your Majesty would have made a Bishop the last year?