Amoxicillin/clavulanic acid (875/125) for 7 days + a week later doing a laser hair removal session?

Yes, you can have laser hair removal while taking these medications, but amoxicillin can cause photosensitivity. It's always recommended to limit your sun exposure when undergoing laser hair removal,and to limit tanning 2-4 weeks before and after treatments. Sun protection is essential. See an expert. Best, Dr. Emer

Augmentin, which is what you are taking, should not be a problem with LHR.  There are other antibiotics which can be a concern, but it doesn't seem you are on those.
One week stopping the antibiotic is also perfectly ok.