Mix coconut milk, chicken stock, curry paste, soy sauce, fish sauce, brown sugar, and basil in a bowl with a whisk until smooth. Set aside.
Turn on a multi-functional pressure cooker (such as an Instant Pot) and select Sauté function. Heat oil in the pot. Add chicken and sauté, stirring occasionally until browned, 3 to 4 minutes. Add lime zest, ginger, garlic, and jalapeno to the pot and cook, stirring, for 1 minute. Press Cancel.
Pour coconut curry mixture into the pot and stir well with a wooden spoon, scraping to loosen any browned bits from the bottom. Close and lock the lid. Select High pressure according to manufacturer’s instructions; set timer for 6 minutes. Allow 10 minutes for pressure to build before the cooking time begins.
Release pressure carefully using the quick-release method according to manufacturer’s instructions. Unlock and remove the lid. Select the Sauté function once more. Add snow peas and bell pepper and cook until vegetables are crisp-tender, 3 to 4 minutes. Press Cancel. Garnish curry with chopped cilantro.
For more of a kick, you can double the jalapeno and add an additional tablespoon of curry paste.