This paper proposes the use of motion primitives on a spherical surface for controlling tethered aircraft. A fundamental constraint of tethered aircraft motion is the restriction to move on a spherical surface. This leads to complex dynamics which are challenging to control, especially during take-off and landing maneuvers. To address this issue, we utilize motion primitives, predefined motion patterns that simplify trajectory control design. By formulating the control problem in a cylindrical coordinate framework associated with the motion primitives, we leverage the minimal influence of periodic variables to enable linearized control models that can comply with demanding requirements. A dynamical model and control architecture are developed, enabling the use of standard multivariable control techniques. Simulations confirm the effectiveness of the approach, demonstrating accurate reference tracking and smooth transitions between primitives, highlighting their potential for tethered aircraft control, especially in airborne wind energy systems.