Part of Chapel Level will be closing ALL of next weekend (12th-15th Oct) from 6pm Friday Night to 6am Monday Morning. The section they are closing completely is between the two sets of lights at the bottom of Dunnikier estate.
If you are travelling westwards (towards the retail park) you'll be diverted down Hendry Road, along Templehall Avenue and then up Fair Isle Road. Add at least 5 minutes to your journey times in this direction. Note: there are shorter routes, but they won't want to flood the side-streets.
If you are heading eastwards (along from the Retail Park to the High School), you'll be diverted up along Rosemount Avenue. This may seem the simpler diversion, but there may be queues coming out next to the Crematorium end if people are trying to turn right to get back to Hendry Road. They may put up temporary lights to cope.
It's not clear if you'll be able to exit/enter the estate in both directions, so give yourself plenty of time if you need to be somewhere!
I believe that this closure is to allow them to "join up" the top and bottom parts of the roundabout that are already built, but it may just be to join up the existing road either north or south so a diversion can be put in place while they finish it later. They'll be working night and day, so there will be a lot going on.
The council have made it very difficult to add links to their website, so Google "fife direct road closures and diversions" and choose "Planned Roadworks" in "Kirkcaldy"