An electronic device may be provided with upper and lower housing portions that are separated by a gap. Hinge structures may allow the upper housing portion to rotate between a closed position and an open position. A flexible printed circuit in the electronic device may be coupled between components in the upper housing portion such as the display and components in the lower housing portion and may span the gap. A hinge gap cover may cover the gap and may overlap the flexible printed circuit to block the flexible printed circuit from view when the upper housing portion is in the closed position. The hinge gap cover may be formed from a layer of radio-transparent material that is rotatably coupled to the upper housing portion and that is biased towards the lower housing with a spring structure.