Simply, there would have been no Princess of Wales.
Caroline of Ansbach ceased to be the Princess of Wales on 11th June 1727 when she became Queen Consort when her husband became king.
When George II became King, his eldest son, Frederick Louis became the Prince of Wales as the title is traditionally granted to the heir apparent to the British Monarch.
When he married Augusta of Saxe-Gotha on the 17th April 1736, she automatically became the Princess of Wales. Upon her husbands death, Augusta became the Dowager Princess of Wales until her death on 8th February 1772.
The title of Princess of Wales was then not held until 8th April 1795 when Caroline of Brunswick married George, Prince of Wales who would later become King George IV.
The title Prince of Wales is traditionally only held by the Heir Apparent, and so there has not been a Princess of Wales without a Prince of Wales. With the recent changes to the law regarding succession to the throne, it may be that in the future the title may be held without a Prince of Wales.