Witchwood's release today will introduce a new card, Genn Greymane. This card reduces the cost of your hero power to 1 for the entire game. If your hero power is upgraded or changes, say with a Justicar Trueheart or through a Death Night, will this new hero power still cost 1 mana, or go back to 2?
Your hero power will return to costing (2) mana. This is evident from the text reading
your starting Hero Power costs (1).
(emphasis mine). This is consistent with the effect of Justicar Trueheart which only upgrades the basic hero power you have at the beginning of the game*. If you play her after you become Jaraxxus she has no effect.
*If you change your baisc hero power with Sir Finley Mrrgglton, the new one you choose will be able to be upgraded by Justicar. I don't believe this special case will carry over to Genn Graymane as the cost will likely reset as soon as your hero power changes.