A Warlock who chooses the Archfey patron gets the Fey Presence feature at level 1 (PHB, p. 109). The PHB says this ability, when used, lasts “until the end of your next turn”:
Starting at 1st level, your patron bestows upon you the ability to project the beguiling and fearsome presence of the fey. As an action, you can cause each creature in a 10-foot cube originating from you to make a Wisdom saving throw against your warlock spell save DC. The creatures that fail their saving throws are all charmed or frightened by you (your choice) until the end of your next turn.
Once you use this feature, you can’t use it again until you finish a short or long rest.
When a character uses the power out of combat, how should this be handled by a DM? How long does it last? Should “your next turn” be interpreted as the player's turn?