Welcome to the Bunnings Workshop community @rbrow. It's fantastic to have you join us, and many thanks for your question about removing a tap handle.
The first thing to check is whether there is a cap on top that unscrews. Typically it will be the thin section with the H on it above the handle's cross bars. This will be a cap that unscrews anti-clockwise and might require the use of multigrip pliers. Use a rag over the tap head to prevent the tool from scratching the finish.
Another option could be a concealed nut under the tap head and usually, that would require a tap key to undo. You'll find the tap key in this Kinetic Spout And Handle Repair Kit. Have a look up under the tap head to see if there are a couple of slots in a nut.
Try these two solutions and then if you don't have any luck let me know.
Mitchell
