This study focuses on the importance of the relationship between carbon and oil in the context of global climate change and energy transition. In particular, this paper explores the link between fluctuations in the price of Brent crude oil in the United Kingdom and changes in the European Union Emission Allowances (EUA), which has significant implications for insight into energy market dynamics and policy making. This study uses an autoregressive (VAR) model to analyze the dynamic relationship between the European Union Emission allowances (EUA) market and the oil market from 2018 to 2024. Through Augmented Dickey-Fuller (ADF) stability test, the VAR model is established, the optimal lag order is determined, and the impulse response and Variance decomposition are analyzed. The results show that the EUA market has a short-term positive impact on the response of the oil market. But this effect has diminished over time, indicating the market's ability to self-regulate and stabilize. These findings provide new perspectives for understanding the interaction between global energy markets and environmental policy tools. The findings highlight the importance of considering these market dynamics when developing market strategies and environmental policies.