From the time the liaison officers of both coalitions met in July 1951, until the armistice agreement was signed in July 1953, the Korean War continued as a stalemate.

Both sides had given up trying to unify Korea by force and the movement of armies on the ground never again matched the fluidity of the first year of the war. 

Source: Britannica

The principal battles of the stalemate in 1951 included: the Battle of Bloody Ridge (18 August–15 September 1951), the Battle of the Punchbowl (31 August-21 September 1951) and the Battle of Heartbreak Ridge (13 September–15 October 1951).