As a new banjo player, once you master the left-hand open-string pull-off, you can use that same skill in a way that's unique to clawhammer banjo. In this new technique, the left hand is the same as what you play for an open-string pull-off, but you don't pick the string with the right hand at all. It's only the motion of your left-hand finger that creates the note.
This kind of pull-off is played almost always on just the 1st string. Luckily, this technique is more difficult to describe than it is to play! Here's a step-by-step guide on how to execute this exclusively clawhammer-style pull-off:
Touch the 1st string with your left-hand middle finger just below the 2nd fret.
You don't have to exert as much left-hand pressure as you need when you're fretting the string, but you do need to have enough contact with the string to create the sideways motion that you'll need for the pull-off.
Without striking the string with the right hand, pull off the 1st string with the middle finger of your left hand, moving down with the finger away from the banjo neck.
You hear just the sound of the open string. Because a note isn't actually fretted, many players simply grab the string with their left-hand finger (without actually bringing their finger all the way down to the fingerboard) and pull down from the 1st string away from the neck.
This shows you an exercise to get the right hand flowing with these pull-offs. To begin, establish a steady rhythm by repeating the basic clawhammer stroke as many times as you need to until you can play it almost without thinking about it. Then add the 1st-string pull-off without changing your right-hand sequence or rhythm.
You can hear this technique in the audio track 1st-string Clawhammer Pull-offs.