She received threats on social media regarding her pay-off when the new super Council takes over in April.
Trevor Lunn MLA said: “I am very concerned at these threats that have been made against Ms O’Connor. She should be able to carry out her duties without having to fear for her safety.
“My thoughts are with Sharon at what must be a very stressful time. I hope that the Police will catch those responsible and I would urge anybody with any information to contact the PSNI or Crimestoppers.
“I hope that every member of Derry City Council will strongly condemn these threats and give her their support.”