How to tighten loose door handle
If you unscrew the metal ring, it will expose three or four screws - check those screws are tight. If necessary, replace the screws with slightly thicker ones and/or pack the screwholes using something like matchsticks.


own work CC BY-SA 3.0 redgrittybrick

Those screws tend to work loose - I just went and tightened up mine! In my case the original fitter was a bit  parsimonious with the screws - I might add more screws in the unpopulated hole positions later.

The set-screw/grub-screw on the underside of the handle, secures the handle to the spindle -- an unseen brass or steel bar of square cross section that passes through the door and thus through the mortice-latch mechanism. Tightening this set-screw is insufficient to make the handle feel firm and properly secured.

If the transverse grip of your handle is loose on the visible shaft, you may need to replace the whole handle. Dismantling the whole thing and taking it apart may reveal a fixable cause of the problem.