If a person is staying on the property that has a warrant can the police come into a locked gate without a search warrant?
If the person with the arrest warrant lives in that home, then yes, the police can come inside the gate. There are some restrictions on what times of day a misdemeanor arrest warrant can be served but a felony warrant can be served at any time and is limited only by general reasonableness.
If the person with the arrest warrant does not live in the home, then the officer cannot enter pursuant to that person’s arrest warrant alone. They would need either exigent circumstances (basically an emergency) or they would need a warrant describing the third party’s home. But if the police violate this, it is the third party homeowner’s rights that are violated, not the arrestee, so it will probably not lead to suppression of evidence.
One final thing to consider is how far the gate is from the home (and I’m just assuming this property contains a residence somewhere). Surprising to many people, the police can usually enter fields and large open yards without a warrant. If the locked gate was between a house and a garage, then the police would need a warrant. If the locked gate opened to 160 acres of barley, it’s a little murkier.