Jerry Graham has taken over the post vacated by former chief constable Craig Mackey in January 2012.
Mr Graham, who was previously Cumbria's deputy chief constable, said the force needed to save more than £10m over the next two years.
The force is predicting an overall loss of 64 officer posts by 2017.
Savings of more than £14m have been made over the past two years from the force's annual budget of about £100m.
Mr Graham said: "Austerity is by far the biggest challenge I will have to deal with.
"What the public of Cumbria want to see is a police force that they can easily access and one that responds to them. That is becoming increasingly difficult.
"Since 2010 we have already saved £14m of our budget of about £100m and we have to find a further £10.5m over the next couple of years, which is a massive challenge.
"We're going through a huge organisational change at the moment and I want the public to see as little change as possible."
Mr Graham said he was also pushing through a revised code of ethics for the force, with the backing of police and crime commissioner Richard Rhodes.
Mr Graham began his career in 1985 with the Lancashire force, before moving to Cumbria as assistant chief constable in 2009.
Cumbria's new chief constable says providing a "visible and effective" police presence amid ongoing austerity is the biggest challenge he faces.