entrench
ɪnˈtrɛn(t)ʃ
ɛnˈtrɛn(t)ʃ
verb
establish (an attitude, habit, or belief) so firmly that change is very difficult or unlikely.
ageism is entrenched in our society
establish,settle,ensconce,lodge,set,root,install,plant,embed,anchor,seat,station,dig in