Loose tap handle

My bathroom sink tap handle is a tad loose and wobbly, I thought the screw on the top shown in the pic just needs to be tightened, but no affect nor can i take it out, screw just seems loose and rotates easily. Do I have a defective screw thread or is there another way the tap handle can be tightened?

That's no the screw.. That's just a little cover.. You need to pull that off and find a hole .. In the hole is the screw, probably needs a small hex driver / allen key,

Beware though, it's a plastic "cartridge' inside these which deals with the mixing hot & cold .. That's probably what's actually bust and loose, the metal handle is attached to that. (to the square post in the thing in the link below)

Something like this .. (but there a few variations)

https://www.hornbach.ch/shop/Cartouc...4/article.html