• High on the new government's agenda will be navigating sensitive ties between global superpowers and geopolitical rivals, the U.S. and China.
• Labour leader Keir Starmer has pledged to improve the "botched" U.K.-EU trade deal, while insisting there is no case for rejoining the bloc.
• The new government will also be looking to bolster the U.K.'s national security in the face of increased global threats.

LONDON — The incoming U.K. government will confront a complex international landscape after Britons head to the polls on July 4.

Labour leader Keir Starmer is widely expected to lead his party to victory, pledging to kick-start a "decade of national renewal," following 14 years of rule under the Conservative Party.

But the center-left politician will also be seeking to redefine the U.K.'s international image in the wake of Brexit, a recent spat of domestic political and economic blunders, and a more fractured global landscape. CNBC takes a look at the foreign policy priorities for the incoming government.

Navigating U.S.-China trade tensions

High on the new government's agenda will be maneuvering sensitive ties between global superpowers and geopolitical rivals, the U.S. and China.

Labour will be eager to maintain Britain's so-called special relationship with its trans-Atlantic ally, presenting a united front in areas of shared strategic interest. But it will also need to adapt to a more protectionist and likely unpredictable U.S., particularly in the event of a change in leadership following the November presidential election stateside.

"You could imagine that the relationship between the incoming personalities of Keir Starmer and Donald Trump would be awkward," David Dunn, professor of international politics at the University of Birmingham, told CNBC over the phone. "But they will work together."

Progress on a U.K.-U.S. free trade deal — one of the key pledges of the Brexit campaign — is also likely to be limited, given current interest from both the Republican and Democrat administrations. Britain could instead be expected to focus on certain "sector agreements" and to continue partnerships on military and critical technologies, Chatham House directors Bronwen Maddox and Olivia O'Sullivan said in a May note.

Faced with a more assertive China, Labour is likely to continue the U.K.'s current position of "deliberate strategic ambiguity," Dunn said, mindful of the country's economic ties to Beijing even amid geopolitical and national security concerns. Labour ministers — like Tories — met with Chinese-founded fast-fashion giant Shein ahead of a potential London listing despite disputes over its human rights record.

"Britain is in a remarkably ambiguous position — as is the EU — dependent on China, but also concerned about territorial acquisition and regional threats," Dunn said.

Repairing EU relations

Labour is also likely to foster a closer working relationship with the European Union.

Starmer, who campaigned for the Remain movement not to depart the bloc in the U.K.'s 2016 referendum, has said there is "no case" for rejoining the EU, including its single market and customs union. He has nevertheless pledged to improve the "botched" U.K.-EU deal, including in areas such as trade, research and security.

"There may be opportunities to revisit the core elements of the trading relationship – not immediately, but after the two sides have rebuilt trust and the relationship is working more smoothly," Mujtaba Rahman, Eurasia Group's managing director for Europe, told CNBC by phone.

The U.K.'s steadfast support for Ukraine amid Russia's full-scale invasion has also helped soothe ties with EU neighbors, establishing its post-Brexit role in bolstering European security. This stance looks set to be upheld under a Labour government.

"This support has strengthened the U.K.'s conversation with EU countries about common risks, in turn opening up the chance for more constructive discussion of post-Brexit relations," Chatham House's Maddox and O'Sullivan said.

Improving national security

Boosting the U.K.'s national security will also be a key priority for Labour amid rising global tensions and the ongoing wars in Ukraine and the Middle East.

In its election manifesto, Labour mirrored Conservative plans to increase defense spending to 2.5% of gross domestic product, but replaced the 2023 timeline with ambitions to deliver the target "as soon as we can."

Given the current geopolitical landscape, however, Chatham House advised this defense expenditure should be raised to a minimum of 3%.

Starmer has also said that Labour will "maintain an unshakeable commitment to NATO and our nuclear deterrent, and put a renewed focus on improving morale in our armed forces." However, discussions over the future shape the trans-Atlantic military alliance are likely to continue into the next U.S. administration.

Strengthening international order

A more general priority for Starmer may be to establish Britain as a stable force in a year of global elections and political flux.

"There's an attempt to be a pillar of stability in a changing world," Dunn said, adding that Labour could present a counterweight to shifting political sentiment in Europe and the U.S.

"Britain did its populism early. Whereas much of the rest of the Western world is moving right, the U.K. is moving left," he said.

Those areas of influence are likely to include diplomacy, security, and international law and order, where the U.K. already has established expertise, Chatham House directors said.

"The U.K. should play a consistent role on global issues where it has credibility – particularly on climate change, international development, arms control and technology governance," Chatham House's O'Sullivan and Maddox added.