Wash the celery stalks thoroughly, remove any tough outer strings if desired, and cut them into jar-length sticks.
Place garlic cloves, dill sprigs, mustard seeds, and peppercorns into clean glass jars before adding the celery pieces.
Arrange the celery sticks upright inside the jars, packing them neatly while leaving enough room for the brine.
Heat vinegar, water, salt, and sugar in a saucepan until all seasonings dissolve into a clear pickling liquid.
Pour the warm brine over the celery sticks until they are fully covered.
Allow the jars to cool before sealing them tightly and placing them in the refrigerator.
Let the celery pickle for at least 24 hours before serving, giving the flavors time to develop while keeping the vegetable crisp.