Police Commissioner Richard Chambers said Fleming was the 34th police person killed on duty.
"I've spent some time here since obviously since New Year's Day and the impact on our frontline staff in particular - who relied on Lyn as a mentor, as the boss - has been significant. Particularly I've noticed for those staff who this is the first time they've experienced a colleague pass away in the line of duty doing what we do as police officers."
He said he was "incredibly proud" of his staff, not just in Nelson but across the country.
"Policing is tough. It's getting more and more volatile, yet we have a job to do for the community and sadly as happened here on New Year's Day, just by doing our job. Lyn, she was there with her colleagues and she's lost her life.
"[It's] very very tough on all of us, a remarkable woman we have lost."