Arcane Shift - if you move a solo unit to an occupied battlefield and then in your first action, you use Arcane Shift, can you replay the unit in the same battlefield?

Yes, you can replay the unit to the same battlefield, provided the battlefield is currently contested (i.e., you are in combat there).

According to the established rulings for Arcane Shift:

• Contested Status: If you move a unit to an occupied battlefield, that battlefield becomes contested. As long as the combat is ongoing, you maintain control of that battlefield, even if your unit is temporarily banished by Arcane Shift.
• Replay Location: Because you maintain control of the battlefield throughout the showdown, you are permitted to play the unit back to that same location.

Important Nuances:

• Combat Requirement: This interaction relies on the fact that you are in a showdown/combat. If you were to use Arcane Shift at a battlefield that is not contested (e.g., a battlefield you control where no combat is occurring), you would lose control of that battlefield the moment your unit is banished, and you would be unable to play the unit back to that location.
• Targeting: Remember that Arcane Shift requires you to target both a friendly unit (to banish) and an enemy unit (to deal 3 damage). You must have valid targets for both to play the spell.

This ruling is consistent with the FAQ regarding Arcane Shift during combat: "You maintain control of the battlefield during the showdown and can replay the unit to that battlefield. The player who controls a battlefield at the beginning of a showdown maintains control until the showdown is completed, even if they temporarily have no units there."