No new appraisal is obtained, relying on an existing one. Is this notice (Right to Receive Copy of Appraisal) required to be given on the refinance (new loan)?

On a refinance - yes.

2. Renewals. Section 1002.14(a)(1) applies when an applicant requests the renewal of an existing extension of credit and the creditor develops a new appraisal or other written valuation. Section 1002.14(a)(1) does not apply to the extent a creditor uses the appraisals and other written valuations that were previously developed in connection with the prior extension of credit to evaluate the renewal request.