An all too common scenario at beginner climbing areas is a new belayer attentively clutching the rope with both hands, while their partner is sketching upwards toward the first bolt or gear placement.
Until the leader clips the first bolt or gear, your job as belayer to spot them like they’re bouldering. Both your hands should be up, thumbs tucked into your palm, and your main task is to keep their head from hitting the ground should they fall before they clip.
Anticipate how much rope is needed from the ground to the first clip or placement, and feed enough rope through your belay device so the leader is never restrained while moving or clipping.
The moment they clip, you instantly change to belay mode, with your hand on the brake and feeding rope as usual.
Of course, this is a non-issue if you’re using a stick clip when sport climbing to attach the rope to the first bolt.
Here’s (more or less) how to do it. Note the climbing rope in the right hand, ready to return to belay mode right after the leader makes the first clip.
And this video, starting about 1: 32