travelling or itinerant
said of a teacher, e.g. a music teacher: unattached to a particular school; teaching in various schools
(Peripatetic) Aristotelian
peripatetically adv
peripateticism /-siz(ə)m/ noun
[early French peripatetique from Greek peripatētikos, from peripatein to walk up and down, discourse while pacing (as did Aristotle), from peri- + patein to tread]