Psyche! & Nar-Sheptha

Nar-Sheptha
Banu Haqim

Unique wraith with 1 life.
While this vampire is in combat, you get +2 hand size, and the opposing minion is considered the acting minion.

Psyche!
Celerity

Press.
Only usable at the end of a round when both combatants are still ready and combat is about to end. After this round, begin another combat with the opposing minion.

Does Combat actually end before a Psyche is played? If so, does the minion with Nar-Sheptha discard down because they lose the +2 hand size outside of combat and then draw back up to +2 hand size when combat restarts?

No, Psyche is a combat card and is played during combat ("at the end of a round"). But I think you still need to discard between combats.

Usually, if both minions involved in combat are still ready and neither side has played a Press to continue, combat is "about to end".
It is in this window, when superior Psyche! can be played.
After playing this card (and maybe other effects), the combat ends.
All effects that were active "while in combat" end as well (e.g. discard down to regular handsize).
Immediately afterwards, another combat starts triggering again all effects "while in combat".