The area where Petersfield ward is now was previously part of Barnwell Priory. The Barnwell Enclosure Award of 1811 gave Bradmore Field to Sir Peter Burrell (Lord Gwydir), after whom Gwydir Street and possibly Petersfield are named.[source]
Petersfield ward was founded in 1968, when St. Matthew’s ward was divided into Market and Petersfield.
Read more on the Gwydir Street website.