Korea is striving to expand renewable energy capacity across the country. However, in response to various challenges, the Korean government has revised the existing strategy to incorporate other carbon-free energy sources, including nuclear power, to advance the energy transition. Nuclear power plants currently operate as baseload units owing to reliability and economic consideration, but flexible operation is becoming necessary to support the growing integration of renewable energy. This study examines the transition of Korea's nuclear power plants from baseload to flexible operation. Based on Korea's electricity supply and demand framework plans, this study assesses the effects of flexible nuclear operations on annual renewable energy output curtailment and fuel costs for 2030 and 2036 through power market simulations. Additionally, grid stability implications are evaluated using a power system simulator. The findings show that flexible nuclear plant operations can help mitigate output limitations and improve grid stability by providing flexibility and reserves. However, the provision of reserves from nuclear power plants incurs increased fuel costs due to the additional consumption of fossil fuels. While the flexibility of nuclear power contributes positively to carbon neutrality by increasing renewable capacity and improving grid reliability, increasing the flexibility of nuclear power plants may inadvertently increase the reliance on fossil fuel. This tendency, in turn, could increase overall fuel costs and carbon emissions, posing a challenge to achieving carbon neutrality.