Are you sure the stairs is "chipboard"? I think you probably mean MDF, the stair treads and risers being made of this and the strings being made of solid wood. It's difficult to make effective repairs in this case without access to the underside. It's usual to tap in loose wedges/ extra wedges and use a combination of glue and screws to tighten up any loose joints. Failing access to the underisde you can try to use glue (perhaps one of those speciality glues like "Chair Doctor"), injecting it into open joints.