Now that Mr Donald Trump has won the US presidential election, it is high time for him to bring an inward-looking "America first" movement to a close and start talking of America's role as a globally engaged leader.

Asia hopes Mr Trump's provocative, isolationist campaign rhetoric will not be implemented as policy by the incoming administration. The region is rife with major geopolitical hot spots - China's rise, maritime disputes in the East and South China Seas, instability on the Korean peninsula and a recent trend of tensions between South-east Asia's strongmen leaders and Washington. Were America to withdraw, it would destabilise the region and cause a split between Asia and the Pacific.

The "American dream" as the world has come to admire it, is not based on protectionism but the universal liberal principles of freedom, tolerance and openness that the United States has long championed. America has not always lived up to them but it has always set them as an ideal to be reached, and others have followed. As the world's economic and political centre of gravity shifts to the Asia-Pacific in the 21st century, the path that the region takes is still up for grabs - with wider global implications. If America refuses to participate in the process of building the regional architecture, it will be relegated to a rule taker, and these are rules based on another vision.

So what does the Asia-Pacific hope for in a Trump presidency?

First, the region hopes for an acknowledgment that the liberal international order has benefited the US. In the great game now under way in the Asia-Pacific, China's long-term strategy is one of undermining and overturning this rules-based order. However, the greater existential challenge to the current order is internal. Across the developed world, there is growing popular opposition to globalisation. By setting a gold standard in the Asia-Pacific, America can play a key role in upgrading the liberal international order to be smarter and more equitable.

The much maligned Trans-Pacific Partnership (TPP) agreement could have been a gateway for America to be at the heart of this process. Without it, China can push its own Sino-centric trade deals, such as the Regional Comprehensive Economic Partnership (RCEP), that exclude the US. This plays right into Beijing's hand - a "divide and trade" approach towards the region. In recent weeks, we have witnessed its success with Thailand, Philippines and Malaysia boldly posturing a separation from Washington. Mr Trump must be careful not to further provoke such departures with a "my way or the highway" response.

Rather, his administration should look to engage with Asia through alternative avenues, even if it rejects the TPP. Forums such as the Asean-US Special Leaders' Summit, Apec and the East Asian Summit fulfil a similar function of US integration and participation in open regionalism.

During the Obama administration, America's allies such as Japan have been frustrated with the US' overly accommodating and sometimes erratic attitude towards Beijing. Mr Trump has made clear his views on China as the source of many of America's problems today. In line with this belief, his administration may take a more principled and hard-headed approach to engagement.

The US should not work on Asia; it must work with Asia. In other words, the US should frame a regional policy for Asia ahead of a China policy. Tokyo, for example, would welcome an approach that precludes a US-China G-2 special relationship.

This is where the US' key allies come into play. Mr Trump has been critical of America's allies, suggesting that they have not been paying their fair share. With financial troubles at home and on the back of unpopular interventions in the Middle East, it is harder to convince the American people of the necessity to sustain the global alliance network in its current form. While America must not forget that its power derives from its global reach and access, partners in Asia also have a responsibility to show greater leadership as geopolitical challenges grow in complexity. Initiatives such as the South Korea-Japan agreement on comfort women issues, Japan's civilian coast guard capacity-building, and the potential Indonesia-Australia joint maritime patrols should be a growing feature of a new autonomy shown by US allies in managing the region. These are the qualitative steps that America's partners must take to change the image of a one-sided relationship.

Equally, allies can contribute further in terms of political capacity. As America's closest ally, Japan has an opportunity to act as a bridge to leaders such as President Rodrigo Duterte of the Philippines. The US should also leverage Japan's attempts to reshape the geostrategic environment. Despite opposition from Washington, Japan has pushed ahead with fostering closer ties to Moscow. Prime Minister Shinzo Abe's stable government and personal understanding with President Vladimir Putin has facilitated this emerging rapprochement. Whether it is balancing China, responding to North Korea or meeting the region's energy and security needs, Japan recognises that Russia should be incorporated into an Asia-Pacific regional framework. In a possible departure from the current US policy towards Russia, Mr Trump believes that he can build a rapport with Mr Putin although as previous presidents have found, this won't be easy.

Mr Trump must also urgently deal with unrest on the Korean Peninsula. North Korea has conducted two nuclear tests this year. The South Korean government is in disarray and the changeover between the Obama and Trump administrations could spell a political vacuum for some months. Mr Trump has previously assured people that he will handle any "madmen" in North Korea, and now is the time to plan for any contingencies during this time of transition.

Finally, Mr Trump needs to pick his team wisely. Institutions and relationships built over time and based on familiarity are especially valued in Asian diplomacy. The challenge here is that if he overturns the foreign policy establishment, he will find it hard to put in place people with the necessary networks. His choice of trade representative will be of particular importance as it is a symbol of whether the US is willing to engage or pull back.

• The writer, former editor-in-chief of the Asahi Shimbun, is chairman of the Rebuild Japan Initiative Foundation, a Tokyo-based think-tank.