How or where do you get more Aristocrat Keys?

You can buy more with the purchase of more gold.

Aristocrat keys are earned by doing dailies, or through the purchase of various packs. You only earn 3 per day from doing your daily quests, so it's completely natural to have more chests than keys.

There is a $5 pack in the in-game store that gives 25 keys each purchase, so if you're interested in opening them all, that would be the only way. Remember, however, that these keys can open any tier of chest, from 1 to 4, so opening any chest lower than 4 is a waste!