Preheat the slow cooker if necessary; see the manufacturer's instructions. Put half the onion, carrot and celery in the base of the slow cooker pot. Arrange the herring fillets on top then cover with the remaining vegetables.
Add the tarragon, bay leaf, vinegar and sugar, then pour over the boiling water. Add the peppercorns and a little salt. Cover with the lid and cook on high for 1½–2 hours.
Spoon the fish, vegetables and a little of the cooking liquid into shallow bowls, halving the fish fillets if liked. Garnish with tarragon sprigs. Serve with pickled beetroot, dill cucumbers and bread and butter, if liked.