Is it possible to trade a player after the playoffs, but before the expansion draft?

No, I don’t think so.

You can trade a player at any time, as far as I know, the trade deadline is just for playoff roster eligibility.

Edit: there is occasionally a roster freeze period. I think there was one around Christmas, iirc.

Yes, if that team in question is out of the playoffs and trading with another out of the playoffs. In facts, you CAN trade someone to a team IN the playoffs but that player won’t be allowed to play

Actually I think it is. Once teams were eliminated this past season they were able to trade players amongst themselves. There were tons of rumours surrounding trades between the bottom teams that missed the playoffs and their limited options and waiting until the playoffs finished to get maximum returns.

Yes, you can make trades once your team is eliminated finished with games, but no trades officially go throw until 24 hours after the cup has been rewarded.

Though there are rules against trading a player to someone for protection and trading to get them back.

If it's the same rules as the Vegas draft, then yes. Multiple teams traded picks to Vegas for player protection.

https://www.pensionplanpuppets.com/2018/12/11/18134244/understanding-nhl-holiday-roster-freeze-toronto-maple-leafs-justin-holl-martin-marincin-trevor-moore