The crossword solution for the term 'intrude gradually' is 'ENCROACH'. To ENCROACH means to gradually enter or take over a space or area that does not belong to you. It can also mean to gradually take away someone else's rights or possessions. Encroaching can be done in a physical sense, such as when someone takes over another person's land, or it can be done in a more abstract sense, such as when someone takes away another person's rights or freedoms.