As near as I can tell, Red Star Rising: The Second Chronicles of Pern is the British release of the novel known in the US as Dragonseye. Of course, it's been a few years since I read Dragonseye, so don't take my word for it.
Red Star Rising chronicles the difficulties facing the inhabitants of Pern as they prepare for Thread to fall- something which has not occurred for 200 years. Two main issues are present in the book: firstly, with their Earth technology slowly slipping away from them, the Pernese must find a way of preserving information for future generations. Secondly, an obstacle to worldwide preparation for Threadfall presents itself in the form of Lord Chalkin of Bitra who refuses to believe that Thread threatens the planet. The story centers around Iantine, an artist with a passion for realistic portrayal of his subjects, Clisser and others at the "College" (what I assume eventually becomes Harper Hall) as they search for ways to preserve information, and K'vin, Zulaya, and other members of Telgar Weyr.
Overall, McCaffrey's characters are well drawn and convincing. However, in my opinion, the book lacks a lot of the fire which made the first couple in the series so compelling. The most interesting part of the book is the fact that the characters are in something of a transition phase- they are no longer "Earthlings" and they are beginning to define exactly what it means to be "Pernese." It is fun to see, especially for someone familiar with both ends of the spectrum; that is, the far future with Dragonflight, and the earliest of the past with Dragonsdawn.