This paper proposes the design of a single linear parameter-varying (LPV) controller for the combined control and smooth transition between two modes in a spacecraft mission. Current industry practice for transitioning between different controller modes is to use a discrete switching approach. When predefined criteria are satisfied, the controller of one mode is turned off and the controller of the other is initialised, resulting in an undesirable transient behaviour. In addition, each controller must individually undergo a rigorous verification and validation (V&V) process. A single controller synthesised using LPV methods streamlines the V&V process and improves the transient behaviour. The proposed design follows a mixed-sensitivity control scheme with LPV weights that are derived from the performance and robustness requirements of the individual modes. The controller is synthesised by minimising the induced L2-norm of the closed-loop interconnections between the controller and weighted plant. The performance and robustness of the controller is demonstrated on an acquisition and pointing task of a flexible satellite through a Monte-Carlo campaign.