Self-explanatory. After my previous question about a sextenary star system and a black hole, I decided to dial back to just two parent stars and a planet. How close could they be if we in the real world still haven't detected them by the early to mid-21st century? The 23rd? I'm assuming they'd have to be farther than Alpha Centauri A and B, since they're the closest stars to us period and were "officially" discovered back in 1592.
The first thing to realise is that binary stars are not at all rare. About one-third of the star systems in our galaxy, the Milky Way, are "multiple star systems", of which the vast majority are binaries. This means that about half of all the individual stars in the galaxy are part of a binary or a more complex system.
If a star is like our sun, it's visible with the naked eye out to about 55 light years. By 1995, the whole sky had been surveyed with sufficiently capable telescopes to spot a star like the sun out to at least 35,000 light years. So a star remaining undiscovered into the future while still being practical to reach via slower-than-light travel isn't plausible.
Hiding the star behind a cloud of dust isn't very plausible either, because there aren't any in the "Local Bubble" region of the galaxy that we're in. Even if there were, stars hidden behind them would be detected by infra-red sky surveys, such as the Two-Micron All Sky Survey, which was completed in 2001.
So having your star be undiscovered isn't plausible. However, just because a star is known, that doesn't mean very much is known about it. What we know about most nearby stars would fit on a sheet of paper for each one. Have a look at the Wikipedia page for Alpha Centauri, specifically the data boxes on the right of the page. That's what we know about the nearest star, which has been studied intensively.
If your star isn't that close by, and isn't especially interesting, it might not get studied intensively. What are the things about it that you want not to have been noticed until your story starts? Why is it important that those things are newly discovered?