The age of the universe is 13.798±0.037 billion years, yet the age of HD 140283 is 14.46±0.8 billion years, how this can be the case?
Wikipedia reports the age of HD 140283 as the figure you cited, 14.46±0.8 billion years. Now look at the reference it refers to. This is the paper by Bond et al that presents measurements of some characteristics of the star and the subsequent calculations, as well as a lengthy section on where the error came from (800 million years is, after all, quite a lot - even in Astronomy!).
The paper describes an approach to determining ages of stars without all that tedious mucking around with globular clusters. It suggests determining "ages of extreme Population II subgiants in the solar neighborhood based on direct trigonometric parallaxes, combined with state-of-the-art theoretical isochrones appropriate to the detailed composition of each star." In short, the idea is to test stars to see if there ages are consistent with the calculated age of the universe (13.77±0.06 billion years - note the much smaller uncertainty).
The paper cites some previous estimates of the star's age - ~14 billion years and 13.5±1.5 billion years. It's worth noting this because the authors appear to pride themselves on how they tried to reduce the error of their measurements. The team next measured the star's parallax, also attempting to reduce error. With that in hand, as well as measurements of temperature and visual magnitude, they used stellar evolution models to determine its age. They also compensated for extinction from their measurements. The authors list the error from parallax, photometry, and extinction as 310 million years. The measurements then (page 11) list the age "implied" by the models and measurements to be 14.46 billion years.
Where is the extra 490-million year-uncertainty? Take a look at Figure 1, near the end. It is due to a variety of factors, the largest of which is the uncertainty of the "initial oxygen abundance" - although more properly the uncertainty in the ratio of oxygen to hydrogen.
It does come down to what David H said - the error measurements due comply with a universal age of 13.77 billion years. I would note, though, that the uncertainty in the measurement of the age of HD 140283 is much greater (800 million years) than the uncertainty of the age of the universe (37 million years). If the uncertainty due to the oxygen/hydrogen ratio could be eliminated, a more accurate age could be calculated, but until this error is addressed (preferably by another team), I think it's safe to say that it's more likely that the measurements for HD 140283 are off than that the measurements for the universe, and so what could have been a paradox is somewhat resolved.
TL;DR - There's a heck of a lot of error in the age of HD 140283, which fits reasonably with current models of the age of the universe, and I would trust the measurements of the age of the universe much more than the measurements of the age of this star, especially because the method used here is not widely used.