Can I use a hollow-wall anchor in between two nearby holes from previous anchors?
I'd advise against even trying. 22 lbs. is quite a lot for a single anchor, and the drywall between the two previous attempts is compromised. I'd not be surprised if it tore right out of a third hole. 

Gypsum wallboard is fairly strong until 1) the paper facing is compromised, and 2) the gypsum material inside is disintegrated. After that, it's mush. 

At this point you have some options, which I'd try in this order:


Ignore it for three days, then decide whether it's actually a problem. 
Adjust or modify the mount on the clock to move its position instead.
Use anchors to mount a thin plate over and below the existing holes. Use an anchor through both the plate and the drywall. 
Open the wall, install a horizontal backer block between studs, and repair the drywall and paint.