The second one doesn't sound right, but the first is awkward too. The following change makes things a bit better, I think: I bought a new goose down jacket yesterday at a shop which is having its biggest ever year-end clearance sale. I am assuming that the identity of the shop is not already known to the reader or listener.
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lucas21cCould you tell me why 'at the shop' makes the sentence sound awkward?"at the shop which is having its biggest ever year-end clearance sale" suggests that the listener should know which shop is meant is from the information that it is "having its biggest ever year-end clearance sale". This may not be what you meant. However, if it is what you meant, th
lucas21cThen, does "I bought a T-shirt at a shop which my brother runs" sound natural if the listener has no information about the shop"?Yes.
GPYThe second one doesn't sound rightIn the OP's second example, it's inserting "yesterday" between the relative pronoun "which" and its antecedent "shop" that makes it not sound right.