The field of Air Traffic Management (ATM) is evolving to meet the growing complexities of air travel, yet traditional systems like Air Traffic Flow Management (ATFM) and Arrival Management (AMAN) still rely heavily on deterministic inputs. This reliance leads to inefficiencies, especially in long-haul operations such as transatlantic flights, where uncertainties in weather, demand, and capacity often disrupt planning. Despite recent advances in machine learning and delay prediction models, integrating uncertainty quantification into ATM systems remains underexplored, limiting their adaptability in dynamic environments. This research seeks to address these challenges by integrating uncertainty quantification into an Extended AMAN and LR-ATFM framework, with a focus on transatlantic operations. The goal is to develop a dynamic speed management system that adjusts flight speeds based on real-time uncertainty predictions. By enhancing predictability and optimizing sequencing, the approach aims to reduce fuel consumption, minimize delays, and improve overall efficiency. This is especially relevant as the aviation industry faces increasing pressures to manage growing air traffic sustainably and reduce carbon emissions.