Earlier this year, she threatened to resign from the role if the review's recommendations were not fully adopted.
Ultimately the changes implemented were watered down and she will step down as chair at the end of the year.
NZR and rugby stakeholders are currently implementing a new governance framework and process for appointing the NZR Board, which was approved at a Special General Meeting in May 2024.
While Dame Patsy's decision not to stand for reappointment is consistent with her position throughout her leadership on governance reform, she said she welcomed the progress made and remained committed to implementing the agreed governance changes.
"NZR has a vital role to play in leading and growing rugby in New Zealand and internationally and it has been an honour to chair the board.
"What's important now is ensuring the appointments process is robust and focused on achieving the best outcomes for rugby, and on continued stewardship of NZR's business-as-usual. These remain priorities for me through to the end of my term."
Dame Patsy and others who are not applying for positions on the new board - including Dame Farah Palmer and NZR president Matthew Cooper - will work in conjunction with the Stakeholder Panel to establish the six-person Appointments and Remunerations Panel (ARP).
The ARP plays a crucial role in the appointment process and will shortlist, interview and select the nine NZR Board members. NZR's voting members will then ratify the appointees in early December.
It is expected that the ARP will be established within the next fortnight, in parallel with the recruitment process closing on October 20.
The appointments process is scheduled to be completed by early December.
The new independent NZR Board is expected to be in place by the end of the year, with Dame Patsy set to conclude her term at that point.
