From my point of view (image is very small and poorly illuminated) you face a hexagonal ending of the shaft, when looking at the top of the tap. My first try was to get a wrench socket, which fits the hexagonal stub. It may be difficult to find a matching wrench socket small enough to fit into the housing of the tap, but you could take a cheap one and grind the outer diameter down until it fits. then you screw it down with a matching screw and insert a short t-handle. Alternatively you may fix a valve handle to it via a sqare axis reaching from your wrench socket into the handle.
Ariser
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