Drain clams into a colander set over a measuring cup. Reserve clam juice (there should be just over 2 cups liquid).

Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Cook bacon until fat has rendered and bacon is crispy, about 5 minutes. Remove bacon to a paper-towel-lined plate; set aside.

Remove and discard all but 1 tablespoon of bacon grease. Cook onion and celery in the bacon grease until onion is soft and translucent, about 5 minutes. Add garlic and cook until fragrant, about 1 minute.

Pour 1/4 cup clam juice into the pan and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Mix in potatoes, carrots, pepper, thyme, and remaining clam juice. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 4 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure using the natural-release method according to manufacturer's instructions, about 5 minutes. Release remaining pressure carefully using the quick-release method, about 5 minutes. Unlock and remove the lid.

Remove 3/4 cup of the potatoes and mash with a fork. Return the mashed potatoes to the pot and stir. Turn on Saute mode. Add clams and half-and-half to the pot and cook until heated through but not boiling. Ladle into bowls and top with bacon.