Catalysis of the reaction: 1-18:3-3-16:0-phosphatidylglycerol = 1-18:3-3-trans-16:1-phosphatidylglycerol + 2 H+. This reaction is the formation of a trans double bond between carbon 3 and carbon 4 (counting from the carboxyl end) of palmitic acid, which is specifically esterified to the sn-2 glyceryl carbon of phosphatidylglycerol.