As a churchman, he was made prebendary of Wells on 8 December 1675, curate of Horspath, Oxfordshire in 1680, and rector of Christian Malford, Wiltshire in 1682.
He was nominated Bishop of Sodor and Man by William Stanley, 9th Earl of Derby on 28 October 1684 and consecrated on 15 March 1685.
On the advice probably of his brother Creswell Levinz, he withdrew his candidature before the election; the manner of his action was criticised as not honourable.
In the account of John Rouse Bloxam, the Vice-President and Fellows of Magdalen wrote on 31 March to Peter Mews, as Bishop of Winchester the college's Visitor; he replied the next day commending Levinz, and advising the fellowship to stick closely to the statutes.
Levinz initially accepted and said he would resist the mandamus of 5 April, by which James sought to impose his candidate Anthony Farmer.