Stake A Claim Meaning

(idiomatic, usually with to) To take an action that asserts a property right in something.

Example:   Who are the nations that have staked a claim to Antarctica lands?
2011 February 1, Mandeep Sanghera, “Man Utd 3 - 1 Aston Villa”[1], BBC:
  Ferguson kept faith in Rooney, even though Javier Hernandez had scored two goals in as many games to stake a claim for a first-team spot, and his decision was justified after only 54 seconds.