Are you talking about an animal villager or a playable character you've made?
If it's a playable character, I think if the design is saved to your designs you can put it on display in the Able Sisters shop (when you walk in there's a stand with random shirts and umbrellas, it's the first stand and it's like a rectangle in the middle of the shop). I don't remember exactly but I think you have to interact with the one you want to replace, if not, then you have to talk to the one who follows you around. You'll be given the option to display designs so you can choose a pattern from the ones you have. I think there's no restrictions about displaying in your shop patterns you didn't make since it's just within your game. Choose to display it as an umbrella or hat, I think that prevents villagers from getting it. Then use your other character to go in the shop and "buy" that pattern, it'll be on their patterns as usual.
If you want to share it with an animal villager, it's harder because it requires luck. You have to display it as a design like a shirt and then hope they'll buy it, but if you do that there's also a chance that other villagers will buy it too.
