Learn Spanish (Latin America): A lo mejor el rey da por concluida la cacería temprano. - Maybe the king considers the hunt concluded early.

This uses the structure dar por followed by a past participle or adjective. It means to consider something as, or to officially treat something as being a certain way. Here, da por concluida means he considers it finished. Notice that the participle concluida acts like an adjective and must agree in gender and number with the noun it refers to, which is the feminine singular la cacería.

Wait, why is it da (indicative) instead of subjunctive after a lo mejor? Doesn't it express doubt?

It does express doubt, but a lo mejor is a strict exception to the usual rule. While expressions of doubt like tal vez and quizás often trigger the subjunctive, a lo mejor almost always takes the indicative in everyday Spanish. That is why we use the present indicative da here.

Could I change the word order and say da la cacería por concluida instead?

Yes, you can. The direct object (la cacería) can go right after the whole dar por + participle phrase, or it can be sandwiched between the verb and por. Both da por concluida la cacería and da la cacería por concluida are perfectly natural. Putting the noun at the end is just a bit more common when the noun phrase is long.

Is there a difference between cacería and ?