With something like that I would make up a caul to help clamp it. Sounds ominous: its not.

Get a piece of scrap wood and cut a v shaped notch in it as close to the angle of the loose piece as you can. Draw round it to mark the cut. Then pad generously before clamping. The more padding the less accurate the cut needs to be! I find bits of old wetsuit are ideal, but anything softish will do. Cork floor tile works. So does layers of rag at a pinch. Put a bit of brown parcel tape on the thing so that it doesn't end up glued to the work.

Most of us have made bigger ballsups than this one! Looking at the break there won't be mega loads on the join, so don't worry too much, any half decent wood glue will be fine. And heck, if the worst comes to the worst and it really doesn't look good enough to you then why not a painted headstock face? On the back the tuners will hide it anyway.