This study investigates the impact of CO$_2$ emission limitations on the connectivity and profitability of a hub-and-spoke airline network, with a specific focus on Schiphol Airport and KLM Royal Dutch Airlines. As sustainability becomes increasingly critical, the aviation industry faces mounting pressure to reduce its environmental footprint without compromising operational efficiency. This research employs a Mixed Integer Linear Programming (MILP) model to simulate airline operations under CO$_2$ constraints. Using synthetic flight data and OpenAP for accurate emissions estimation, the model optimises fleet composition, flight scheduling, and passenger flow while balancing profitability and emissions reduction. The study explores the potential of fleet renewal to mitigate the negative effects of emission caps on both connectivity and revenue. The findings demonstrate that significant emission reductions can be achieved through strategic fleet planning, with minimal impact on the airline's network and financial performance. This research provides a viable framework for integrating environmental considerations into long-term airline planning, contributing to the ongoing efforts to reduce aviation's environmental impact while maintaining its economic and operational benefits.