When I swapped out my dwarven fighter for an elven fighter I'm stuck with a lvl 1 character with only lvl 4 dungeons to do. I can't level my new character without access to lower level dungeons. Maybe set up a fighting pit somewhere that you can go to just fight a couple of rounds for extra xp, or when you buy a new character have them start at the same level as your current lowest character.
lower level characters will gain more experience for completed dungeons, so they will close the gap quickly. if the dungeons are too hard you can buy a new party and level them together, or just go solo with the new one, due to the existing equipment he should be a lot stronger and can finish the first dungeons quickly. later on you can buy lvl 10 chars that save you some of the hassle, but they are also a lot more expensive.
Adventures reset every day, so they will be available again shortly. This is, sadly, most annoying when you first start the game and want to play more. Once you've completed more of the adventures it's less of an issue. Also, you eventually open up a new shop where you can hire level 10 characters (for 100 gold). For leveling up new characters, I suggest trying to beat adventures higher level than the character you want to level up. You can do this with good equipment, or by teaming them with other higher level characters. By beating an adventure 1 level higher they get 15 exp instead of 10. 2 levels higher and they get 20 exp, but that can be a bit more difficult.
