English Medieval Monasteries 1066-1540 by Roy Midmer states that a foundation of Cluniac nuns was founded at Fotheringhay by Simon de St. Litz (aka Simon de Senlis) Earl of Huntingdon circa 1141. The nuns “soon” moved to Northampton (Delapre). However they “retained their church and endowments” until the foundation of the College by the 2nd Duke of York in 1411.
This implies that the original church was built in 1141, although it is entirely possible (perhaps probable) that it incorporated earlier work. Presumably the Delapre nuns had the advowson.
It also seems reasonable to assume that the nunnery buildings would have been on the site later used by the College, immediately adjacent to the church, between it and the river.
What means the 2nd Duke of York used to persuade the nuns to give up their property so he could develop his College is not clear. Were they “bought off” or were they simply “told”? The College had a charter from Henry IV so that may have been the decisive factor.