Flying vehicles are becoming ubiquitous unprecedentedly due to the advancements in aviation and space industries. In addition to already deployed geosynchronous Earth orbit (GEO) satellites, low Earth orbits (LEO) satellites are being deployed in large numbers to provide connectivity to ground users. Furthermore, high altitude platforms (HAPs) stand as another connectivity option for the ground users. Besides, unmanned aerial vehicles, also known as drones, and flying taxis are emerging as users in the sky, which require robust and reliable communication connectivity for their safe and secure operation. Although there are different connectivity solutions specific to certain limited domains, integrated connectivity solutions and a holistic network architecture are vital to unlock potentials of the recent advances and create new services for both ground and aerial users. To this end, 6G for Connected Sky project aims at solutions to enable reliable and robust connectivity for aerial and ground users via flexible and adaptive network architecture adopting multiple technologies such as satellite and direct air to ground communication (DA2GC). In addition, this project focuses on novel wireless network design and management schemes in 3-dimensional (3D) space including different types of flying vehicles with their unique requirements. Another focus is to provide robust, low latency and/or high-capacity communications to ground users in the rural areas without any infrastructure via non terrestrial networks (NTNs). https://www.celticnext.eu/project-6g-sky/