He was on holiday in Shanghai in 2009 when Peiyun Chen, a 20-year-old sex worker, was found beaten and strangled.
Chinese authorities allege Kim committed the crime, but he had left for South Korea before officials sought him for questioning.
A warrant for his arrest was issued in 2010. A year later, after authorities sought his extradition from New Zealand, he was arrested and spent five years in jail, without trial, before being released on electronic bail in 2016.
In today's hearing, his legal team led by Tony Ellis argued the circumstances in China have changed since previous assurances were given back in 2015, and there is a complete lack of transparency in the judicial process that operates largely behind closed doors.
Ellis said his client had been subject to undue delay, and the stress of proceedings had caused significant damage both physically and mentally.
"He's already done eight years of detention, waiting to find out what's going to happen and it preys on your mental health."
If extradited to China, he might not have access to life-saving health care, such as an indicated liver transplant, Ellis said.
Ellis also stated the lengthy wait for Kim would contribute to an unfair trial and that a fair trial under the circumstances "is simply not possible".
Ellis argued the medical and mental deterioration of Kim was significant enough and if the minister ruled against the case of Kim, a further judicial review would be sought.
Defence co-counsel Ben Keith explained there was real concern for their client who may be subjected to undetectable torture techniques, and he was at particular risk because of his fight against extradition.
Keith said there was an obligation on Minister for Justice Kris Faafoi to address the many risks Kim might face if extradited to stand trial, and a failure to do so was "passing the buck".
On behalf of the Crown, Solicitor-General Una Jagose QC, said if Kim was tried and detained in Shanghai, where Chinese authorities say he will be, there were no substantive grounds that he would be at risk of torture.
In response to the defence's point around undetectable torture, such as white torture where sensory deprivation is used to elicit a confession, the Crown contended this was not the place to question the general state of China, but instead the risk to Kim.
The Crown said Chinese authorities would honour fair trial rights, and China understood the concerns of New Zealand courts.
They also argued the threshold for a complete reassessment by the minister was high in terms of new material and the defence's case did not meet this.
Jagose referenced the assurances made by China in 2015, and said the Crown stood by the fact there was no real risk that Kim wouldn't receive a trial that wouldn't meet minimum international standards.
Jagose said Chinese authorities were incentivised to maintain their commitment to honour the assurances made because it was critical for China to be seen as cooperating with international law enforcement so that they can "get what they want" themselves.
The court also heard China had made assurances Kim would have access to medical attention and treatment, as well as access to medical professionals of his choice.
All five Supreme Court Justices will deliver their verdict in the coming weeks.
Court timeline:
2009 – Chinese sexworker Peiyun Chen is found beaten and strangled.
2010 – A warrant for Kyung Yup Kim's arrest is issued by Chinese authorities.
2011 – New Zealand receives a request for the extradition of Kim to stand trial for homicide in China.
2013 – District Court determines Kim eligible for extradition.
2015 – Then Minister of Justice Amy Adams, after seeking diplomatic assurances from China as to Kim's treatment, determines Kim be surrendered to the Peoples Republic of China.
2016 – Kim challenges Adams' decision by judicial review, which is won in the High Court. On review, Adams again finds Kim eligible for extradition to China. A further judicial review is sought and lost.
2019 – Court of Appeal quashes Adams' decision and the case heads to the Supreme Court.
2020 – Supreme Court holds a substantive hearing to hear the appeal of the Crown in the quashed decision and cross-appeal of Kim.
2021 – Supreme Court Judges direct a report be filed regarding issues of torture and fair trial, focusing on the safety of Kim.
TODAY – Both the Crown and council argue their case for extradition.
