Probably read 30+ years ago. The book's plot is VERY similar to "Far Centaurus" by A. E. van Vogt. But when I saw it was a possible duplicate when asking the question, I read it and it is NOT the story I was thinking of.
The plot was virtually the same. but a couple things I remember that are different from "Far Centaurus".
I think the slow ship was "discovered" in route to there destination, by an FTL ship that was regularly travelling the same route. And was "brought" the rest of the way by the FTL ship (or another ship designed to transport it) or the crew were brought and the slow ship left behind.
Society/humanity had advance beyond the slow ship crew so much that the crew would not fit in with the "future" population. Their liaison presents several examples to show that they are just to primitive to fit in. The one I specifically remember was:
He points out a balcony window (or maybe from an upper level of a walkway) to the crowd walking on the sidewalk below. [It seems to me the sidewalk was very wide, maybe instead of a sidewalk it was the lower floor of a shopping mall type passageway. 20-30 feet wide] He directs their attention to a large gap, or bubble in the crowded walkway where no one was walking. (taking up like 1/2 or 2/3rds of the width of the walkway, obviously it would be inconveniencing everyone by having to walk around the space.
He tells them it is a [ Courtesy Circle(?) ] and that, at sometime in the past few minutes or so, someone (1st person) was having trouble moving through the crowd. (Maybe carrying bulky packages, or dealing with small children, etc.) Someone else (2nd person) walking the opposite direction, as a courtesy, moved to the right to allow the 1st person more room to get through the crowd. Then someone walking behind the 1st person, saw the courtesy of the 2nd person, and they also moved to their right, now creating a small space in the crowd. Then someone behind the 2nd person sees the 3rd person and they also move to the right, making a bigger space.
This happens over and over as more people seeing people coming from the opposite direction, displaying acts of courtesy, and they reciprocate, eventually creating large bubbles in the walkway which people are walking around.
One of the slow ship crew says something like, but how could the people walking now know about what happened 20 minutes ago. why don't they just fill in the gap now, so they don't have to crowd against the wall.
And the Liaison says something like: Of course they don't know the cause of the circle, but they are all honoring and showing courtesy for the initial action that caused it to form. That these "Circles" can last hours, and sometimes even days, before they shrink and eventually disappear. And he says that's the point, it's just one example of many ways in which society has advanced beyond you and you will never fit in.
I do not think the conclusion to the story was the same as "Far Centaurus" (time travel back to their own time) I have vague recollections of them being asked to do some "mission" for the future people. (travel somewhere to help with a problem the future people were no longer able to deal with. Like maybe an alien encounter, or starting a new colony)
