In earlier life tutor to Sir Philip Sidney, and interested in the manner of Sidney"s circle in literature and Ramist logic, he became more sternly religious in his opinions. He is now remembered for his 1606 poem Ourania, though not for its poetic merit. He was tutor in Greek to Sir Philip Sidney, and was a student of Magdalen College, Oxford in 1569, graduating Master of Arts in 1577.
He held clerical positions successively at Redbourn in Hertfordshire, Finedon and Titchmarsh in Northamptonshire, Leire in Leicestershire, at Saint Margaret Lothbury and Saint Giles-in-the-Fields in London (1590).
Baxter was one of the signatories to the famous letter addressed to Thomas Cartwright, dated London, 25 May 1577. He became warden of Collegiate Church of Street Mary Youghal, Ireland, in 1592, and was inducted into the office of warden 23 May 1592 by William Lyon.
On 25 August 1597 Baxter found that the revenues of the college were threatened. He was obliged to give a bond that he would, within forty days after demand, resign his office.
On 26 April 1598 complaint was made to the court of revenue exchequer, that Baxter had refused to allow the officer of the court to sequestrate the revenues of the college.
An attachment was issued against him, and a new sequestration issued. On 30 June 1598 Baxter, having resisted the surrender of his office, through third parties disposed of the college revenues and the college house to Sir Thomas Norris, President of Munster. Baxter then resigned.
But the commissioners, finding that the revenues had been disposed of, refused to accept the trust.
Baxter left Ireland in 1599. He is next found vicar of Mitchel Troy, Monmouthshire, and compounding for his first-fruits of the living 26 May 1602.
In 1633 he was engaged in controversy with John Downes, a theologian of Bristol.