I cannot see a direct link. But default might have indirect effects. So, if the US defaults tomorrow, money printing, at least for the near future, will be limited, hence gold might actually fall in dollar terms, although both gold and the dollar would rise against foreign currencies. But there are 1000 other things that could happen, so perhaps there’s no single answer to your question.
If a State defaults on its bond obligations, then demand for such would plummet. People who formerly were willing to invest in State bonds will now prefer to invest elsewhere. Contrary to Merlin, I think the demand for gold (if not commodities in general) would rise due to this “shifting of demand” from State bonds, leading to upward pressure on the price(s).