To encroach is to gradually move or go into an area that is beyond the usual or desired limits, or to gradually take or begin to use or affect something that belongs to, or is being used by, someone else. Encroach is often followed by on or upon.

// Conflicts between people and bears increase as humans continue to encroach on bear territory.

// They argue that the law would encroach on states' authority.

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"In their young adult years, Mufasa and Taka find their courage and loyalty tested when a group of white lions encroach upon the pride." — Lovia Gyarkye, The Hollywood Reporter, 17 Dec. 2024

The history behind encroach is likely to hook you in. The word comes from the Middle English verb encrochen, which means "to get or seize." The Anglo-French predecessor of encrochen is encrocher, which was formed by combining the prefix en- ("in") with the noun croche ("hook"). Croche is also an ancestor of our word crochet; that word first referred to a crochet hook or to the needlework done with it. Encroach carries the meaning of "intrude," both in terms of privilege and property. The word can also hop over legal barriers to describe a general advancement beyond desirable or normal limits (such as a hurricane that encroaches on the mainland).