encroach

Concise Oxford English Dictionary © 2008 Oxford University Press:
encroach/ɪnˈkrəʊtʃ/

▶verb (encroach on/upon) gradually intrude on (a person's territory, rights, etc.).

■ advance gradually beyond expected limits.

– derivatives
encroacher noun,
encroachment noun.

– origin ME (in the sense ‘seize’): from OFr. encrochier ‘seize, fasten upon’, from en- ‘in, on’ + crochier (from croc ‘hook’).