No one's really nailed a successor to Star Control II and an official addition to the series was killed off by the lacklustre Star Control III. Ur-Quan Masters HD, a free remake of SCII based on the original source, might be as close as we'll get to a modern refresh of the venerable title.
Fans of Star Control II are likely aware that there's already a remake out with the same name, just without the HD moniker. Unfortunately, it hasn't been updated since July 2011. This new HD rendition not only provides a new source of updates, but graphical and aural niceties as well. The easiest way to experience them is to check out the video above.
For those who'd like to get tentacle-deep into Ur-Quan Masters HD, a 553MB alpha is available for download at the game's section on SourceForge. Being an alpha, you should expect some rough edges — probably a few, actually — but if you're desperate to fulfil your space strategy/RPG/action needs, there's not much to lose except a chunk off your download quota.
On a related note, there's the in-development Starsector (former Starfarer) if you'd like to check out a modern successor. It's in alpha also and requires the opening of one's coin purse, but it's under constant development and visually, it looks the part.