Brexit does not mean the UK is turning away from the world, Theresa May will tell the United Nations.
But the Prime Minister will acknowledge the political class around the world needs to do more to listen to the concerns of the general public.
In her first address to the UN general assembly, Mrs May will say that "bold action" and international co-operation is required to meet the challenges facing the world.
She will use her appearance at the gathering of world leaders in New York to say that only the UN can cope with issues including terrorism, mass migration and modern slavery.
Mrs May will say that when the British people voted to leave the European Union, "they did not vote to turn inwards or walk away from any of our partners in the world".
But the Prime Minister, who used the G20 summit earlier this month to acknowledge the need to address the anti-globalisation movement's concerns, will return to her theme about a change in the way politics works.
She will say people want "a politics that is more in touch with their concerns; and bold action to address them" and that "the biggest threats to our prosperity and security do not recognise or respect international borders".
She will add that "if we only focus on what we do at home, the job is barely half done".
The Prime Minister will remind leaders that the are at the UN "as servants to the men and women that we represent back at home".
Se will add: "And as we do so, we must recognise that for too many of those men and women the increasing pace of globalisation has left them feeling left behind.
"The challenge for those of us in this room is to ensure our governments and our global institutions, such as this United Nations, remain responsive to the people that we serve. That we are capable of adapting our institutions to the demands of the 21st Century."
She will say that the UN needs to forge a "bold new multilateralism" to address the "big security and human rights challenges of our time".
She will say: "When extremists anywhere in the world can transmit their poisonous ideologies directly into the bedrooms of people vulnerable to radicalisation, we need not just to work together to prevent conflict and instability in nation states but act globally to disrupt the networks terrorist groups use to finance their operations and recruit to their ranks."
Mrs May will say the "unprecedented" mass migration requires "policies that are fit for the challenges we face today".
She will call for cross-border action to tackle criminal gangs "trafficking our fellow citizens into lives of slavery and servitude".
The Prime Minister will add: "This is not the time to turn away from our United Nations. It is the time to turn towards it.
"Only we - as members of this community of nations - can act to ensure this great institution becomes as relevant for our future as it has been in our past."
The challenge facing Mrs May as the UK prepares to leave the EU will be underlined in a meeting with Japanese counterpart Shinzo Abe later.
Earlier this month, the Japanese government produced a 15-page dossier listing the country's concerns over the impact Brexit could have on its firms with bases in the UK.
Mrs May will also hold a series of face-to-face meetings with other leaders and take part in a summit on refugees called by US president Barack Obama.