The PK (Primary Key) has nothing to do with a clustered or nonclustered index. It is a logical structure that gives you a field to uniquely identify a row. It can be a clustered or non-clustered index in its implementation, but they are not the same.
You rebuild a clustered index to deal with fragmentation periodically. You don't need to mess with the primary key, the identity field, or anything else. You just specify the ALTER INDEX REBUILD commands.