Yes. Handle seals are available.
I think you'll need to take the hand off. From inside the door you see a small threaded stud sticking through with a weird kind of clip on it. Undo that.
Then from the outside prise off the plastic covers - first take off your chrom ones. Then the black plastic ones. (I never managed to get mind off in one piece). Then on the outside around the lock barrel there's a threaded tube/ring thing around the keyhole barrel. That threaded ring screws out. Then you can take the handle out through the inside and see it properly.
Or it may be that you just need to tighten up that threaded ring to stop the barrel turning. In any case the outside trim needs to come off so you can see this threaded ring.
This guy is using long nosed pliers to turn that threaded ring I'm talking about. It's got little indents and there's surely a proper tool that sits in those indents but long nose pliers does it.