Diagnosis
The pivot screw inside the hinge has worked loose over time. This is a common wear point from the constant opening and closing.
How to Fix It
You can tighten it yourself. Let the styler cool. Look at the hinge from the side—you'll see a very small, deep hole on the black hinge housing. Use a precision Phillips #00 screwdriver. Insert it straight into the hole until it engages the screw inside and give it a gentle clockwise turn. Don't overtighten; just a quarter-turn to remove the wobble.
If That Didn't Work
If the screw feels stripped or turns without tightening, or the wobble is actually from a cracked plastic housing, the hinge assembly is damaged. Continued use will stress the internal wires. Stop using it and contact ghd support.
Heads Up
Never try to lubricate the hinge with oil or WD-40. It will attract dust and hair, making it gummier, and could drip onto the hot plates causing smoke and fumes.