From Longman Dictionary of Contemporary Englishstake something ↔ out phrasal verb informal1 WATCHto watch a place secretly and continuously → stakeout Police officers have been staking out the warehouse for weeks.2 to mark or control a particular area so that you can have it or use it We went to the show early to stake out a good spot.3 to state your opinions about something in a way that shows how your ideas are clearly separate from other people’s ideas Johnson staked out the differences between himself and the other candidates. → stake→ See Verb table
Examples from the Corpus
stake out• Presumably the house was still empty, and they were staking it out.• It was later spotted in Cambridge, where police staked it out and arrested Kenney when he returned to it.• He'd have Jamieson stake it out for one more night, then he'd have to abandon the issue. 