In season 23, do I have this opportunity to change characters? Of course I know that anytime, but I’m pushing with a monk now and I want to replace it so I can get the kit!
If you mean Haedrig’s Gifts, I’d refer you to the patch notes…
Completing Chapters 2, 3, and 4 of the Season Journey will reward you with three of Haedrig’s Gifts. These contain a few pieces from one of your Class Sets. Players can only unlock one Class Set in this manner per Season across Hardcore and Non-Hardcore, so choose wisely!
In other words, you get one set of gifts, per season, per region, per account. Your have to gear up any and all of your other heroes the usual way, i.e. mob drops, gambling at kadala, upgrades / reforges in the Cube, crafting, sharing drops in groups, and so on.