St Conor's Primary School was officially opened on 1st September 1973, replacing the old Culmore School on the Tamlaght Road.  The staff of seven teachers and 213 pupils moved into a new building on a much larger site on the Brookmount Road with its own spacious playground and playing fields.  Principal at the time was Mr Colm MacRory. The school's enrolment had increased to 355 upon Mr MacRory's retirement in 1983.  This triggered the need for an extension to the original building.
  
Mr Oliver O'Kane, who had served as assistant teacher on the staff of St Conor's from 1973-1975, was appointed Principal in 1983.  In 1985 the school extension was officially opened by Parish Priest, Monsignor Rooney and included five new classrooms, an assembly hall, staff room, learning support room and multi-purpose areas. This decade also saw the introduction of a school uniform (1985) and the formation of the first parent support group (1989).

The Nursery Unit, housed in a separate, self-contained building adjacent to the school was opened in 2002 to cater for up to 52 children in total: 26 in a morning and 26 in afternoon class.  The Nursery Unit secured high quality pre-school provision for the local area.

In September 2003, Mr Neill Barbour, a long-serving member of staff and Vice-principal, was appointed as Mr O'Kane's successor.   Following the retirement of Mr Barbour in April 2007, Mrs Katrina McGettigan (Vice-principal from January 2004) was appointed Principal of St Conor’s Primary School & Nursery Unit.  She took up post in September 2007.

In June 2009 the school learnt that, following completion of the Minister of Education’s review of capital projects, St Conor’s was categorised as ‘’Fully Compliant’’, signalling that the school was deemed viable and sustainable in the long term and is well placed to deliver the full range of Department of Education (DENI) policies into the future. This news was received well by all associated with the school and everyone hopes that capital funding will be made available so that the new school build, on the existing site, can progress.