WordNet sense 1 (an artifact that is inserted or is to be inserted):

inset, inset

WordNet sense 2 (put or introduce into something):

enter, introduce, infix

WordNet sense 3 (fit snugly into):

tuck

WordNet sense 4 (insert casually):

sneak in, slip in, stick in

WordNet sense 5 ((broadcasting) a local announcement inserted into a network program):

cut-in

WordNet sense 6 (introduce):

enclose, inclose, put in