This was a problem before inflationary cosmology, when estimates of universe age could differ with a factor 2. Now the uncertainty is down to the order of parts of percent, same precision with which we date Earth [!], and AFAIK there are no longer any stars that stress the theory. Meaning the 1 sigma results on star ages cover the 1 sigma result of universe age (IIRC).
As usual, these things are just a google away: "The new Hubble age estimates reduce the range of measurement uncertainty, so that the star's age overlaps with the universe's age — as independently determined by the rate of expansion of space, an analysis of the microwave background from the big bang, and measurements of radioactive decay." [
http://www.nasa.gov/mission_pages/hubble/science/hd140283.html ]
That 2013 article covers the history of previous estimates of the age of HD 140283 (if not the history of the precision increase in cosmology).
If anyone star would stress the cosmology, I think people would now start to ask for extraordinary evidence, since it would constitute an extraordinary claim.