Handle assembly comprising a clearance catch-up system for a button

A handle assembly, for a vehicle door, comprising:

• a structure part and a cover part arranged to be mounted on the structure part;
• a pushing device configured to be mounted on the cover part, said pushing device having a button arranged to be accessible from an exterior of the handle assembly through an opening of the cover part, said button being movable between a rest position and a pressed-in position;
• a switching device configured to be mounted on a receiver of the structure part, said switching device including an actuator configured to be moved from a default position to an actuated position when the cover part is mounted in a final position on the structure part and when the button is displaced from the rest position to the pressed-in position;
• and
• a clearance catch-up system configured to displace the receiver from a retracted position, according which the switching device and the receiver are distant from the cover part mounted in the final position, to a deployed position, according which the switching device and/or the receiver cooperates with the cover part mounted in the final position.