Will the next leader in Seoul agree with the United States on key issues including North Korea and the placement of a US-built missile defense system
on South Korean soil? Or will South Korea favor a shift? Will it seek closer relations with China, its largest trading partner?
State Department spokesman Mark Toner characterized Park's ouster as a "domestic issue on which the United States takes no position." He also stressed the close US ties with South Korea as "a linchpin of regional stability and security."
US Secretary of State Rex Tillerson is expected to arrive in Seoul next week.
With Park's ouster, South Korea will hold a snap election within 60 days in what is guaranteed be a campaign frenzy. Opinion polls so far show the left-leaning Moon Jae-in, who lost to Park in 2012, as the front-runner.
Liberals in South Korea typically favor a more conciliatory approach with Pyongyang, and many oppose the US missile defense system known as the Terminal High Altitude Area Defense, or THAAD
, which is designed to intercept incoming missiles, conceivably from North Korea.
Meanwhile, conservatives such as Park have retained a more hawkish view on North Korea and generally support US policies, including THAAD.
"If progressives take power, I do think issues like THAAD and North Korea policy could be on the table, which would have huge consequences for the US right now," said David Kang, director of the University of Southern California's Korean Studies Institute.
After nine years of conservative leadership and a scandal-marred Park presidency, South Korea may be signaling it's ready for a change. The conservatives lost their majority in a shock defeat in parliamentary elections last year.
New leadership in Seoul could mark a shift on two key issues in US and South Korea relations -- the missile defense system and the position on North Korea.
THAAD and China: It's complicated
The first pieces of the THAAD defense system
arrived this week in South Korea. The project has been fiercely opposed by China and Russia as a threat to their security.
China has raised significant economic pressure
on South Korea to scrap the defense system through threats to a South Korean retail group and restrictions on Korean products and possibly travel to the country. These have triggered fears of a trade war, which would be crushing for South Korea since trade with China accounts for about a quarter of its exports.
Regardless of the pressure from Beijing, THAAD already has its share of critics within South Korea. Opposition parties have sought a vote on the missile defense system in parliament once the country's political uncertainty is resolved.
South Koreans generally don't want to weaken the alliance with the United States, but if the next leader walks back on THAAD, "we'd have a real change in the Korean policy toward the US," said Kang, who is also the director of the USC Center for International Studies.
Such a scenario would be a win for China and a blow for the United States.
Regardless of political ideology, South Korean presidents have sought better relations with China.
"Korean politicians, no matter left or right, are more welcoming of China than the Americans would like," Kang said.
There's the question of North Korea
North and South Korean relations have remained frosty during the last two conservative presidencies.
"The South Korean left has been more accommodating of North Korea, more willing to engage. The South Korean right has been more hawkish and more confrontational," said Robert Kelly, associate professor at Pusan National University's Department of Political Science and Diplomacy.
Liberal presidents have supported engagement with North Korea, including what's known as the Sunshine Policy
in which Seoul refrained from criticizing Pyongyang's human rights record and struck a more conciliatory tone.
That era from 1998 to 2008 was marked by fractures in the US-Korea alliance.
The Sunshine Policy ended when conservative President Lee Myung-bak
took power in 2008 and relations on the peninsula have stalled since. Liberal South Korean leaders such as Moon are critical of hard-line policies on North Korea, noting that they have not deterred the isolated regime's weapon testing and nuclear ambitions.
Their belief is that "engaging and interacting with North Korea is the sole way to change their main foe -- and bring long-term peace and stability to the Korean Peninsula," wrote Booseung Chang, a fellow at the Rand Corp.
"In their scheme, one key to the success of this strategy is securing cooperation from Beijing. This change goes against existing US strategy toward North Korea and China."
But calling for engagement with North Korea may not be so easy given last month's high-profile assassination of dictator Kim Jong Un's half brother
and recent missile tests
, Kelly said.
"All this suggests that North Korea is a pretty serious global menace now
, and it'd be really hard for the South Korean left to tell the US that we want to re-engage this country," he added.