Basically a turn player has Priority. That means you have Priority during your turn and an opponent have Priority during his turn.
In Duel Links
Be automatically processed
Players do not have to deal with Priority by themselves since it is dealt with automatically. When a card effect cannot be activated in the game, it is due to Priority or spell speed.
What is Priority transfer?
Priority passes from a turn player to an opponent after conducting specific acts. Additionally, the turn player have to give Priority to an opponent when going into a next phase/step.
Acts having Priority pass from a player to an opponent
Using spell/trap cards
Activating the effects of spell/trap cards
Activating the monster card's effect
Going to a next phase/step
Acts not having Priority move
Some acts do not have a turn player to pass Priority to an opponent, and the turn player can keep holding the right. In that case, the opponent can use a card after the tune player announces passing Priority.