At the end of Avengers: Endgame Steve Rogers
comes back to the present
and brings the shield with him.
How did Steve manage to bring it or even possess it?
I am going in with the assumption that there is only 1 shield. It was buried in ice along with him during the events of Captain America: The First Avenger. He wields it till Captain America: Civil War and leaves it after fighting with Tony. In Avengers:Endgame, Tony gives it back to Steve. It is broken in the fight so Steve wields Mjolnir and takes it back with him at the end when he has to return the stones.
So, where did this extra shield come from?