How can 'HD 140283' be older than the universe? Scientists have known about the star HD 140283, informally nicknamed the Methuselah star, for more than 100 years, since it cruises across the sky at a relatively rapid clip. The star moves at about 800,000 mph (1.3 million km/h) and travels the width of the full moon in the sky every 1,500 years or so, researchers said. Its apparent magnitude is 7.223.

Previous research had estimated that the Milky Way galaxy's so-called
"Methuselah star" is up to 16 billion years old. That's a problem,
since most researchers agree that the Big Bang that created the
universe occurred about 13.8 billion years ago.

Later estimates show that the star could be as old as 14.5 billion years (± 0.8 billion years), which is still it older than the universe's calculated age of about 13.8 billion years. This is an obvious dilemma.

How can a star be older than the universe itself?
It's not - the current age is an estimate. The discrepancy comes from astronomer's attempts to fully and correctly measure aspects of the star, particularly its distance.  From the NASA page:


  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.


Currently, if you take the uncertainty into account, the current estimate for the star's age is 14.5 +/- 0.8 billion years  or between 15.3 and 13.7 billion years - the latter end of the estimate overlaps with the current model of the age of the Universe - so a more correct way of describing this age is that HD 140283 is at least 13.7 billion years old by this estimation.

Another paper based on this star in Nature - "Nearby star is almost as old as the Universe", a team has narrowed down the age to 13.9 +/- 0.7 billion years, stating that:


  Taking into account that experimental error, the age does not conflict with the age of the Universe, 13.77 billion years. 


more concisely stating that


  The star's age is therefore at least 13.2 billion years


No doubt further work is being performed to further refine the age of the star.