To obtain a bear pelt go either to Regent Valley or Wizard's Folly and kill Black Bears until you get one. The bears drop bear pelts even if you don't have this quest so remember to save one of those you get if you haven't done this quest yet. After you have obtained a pelt, return to Alison who will craft it into a cloak. Deliver the cloak to Little Thom in the Barradin Estate to receive your reward.