Why is Saint Clare sometimes pictured holding a bishop's crozier?

She was an Abbess. The title implied the female head of an Abbey. Now the titles used more often are Mother Superior, there are also such female ranks as Provincial ( here a noun, not an adjective) In some cases, Abbesses carried the Crozier as a badge of rank. There was a convent of the Noble Ladies in Prague- in the old Austro-Hungarian Empire- made up of noblewomen- and indeed they had a Princess for an Abbess. Costume combined elements of royalty and religious stature- she , too had a Crozier. These institutions no longer exist as AHE was split up into several republics. arguably the convents- and tombs, etc. may survive.