Whenever a chromosome is replicated the replication machinery passes by the nucleosomes without deleting the histones from the DNA. How this happens is since not fully understood.  Together of the daughter DNA molecules in which result from replication have old histones bound to them but overall, as the amount of DNA has now doubled more histones are needed to package the DNA rightly into nucleosomes.  Not surprisingly, therefore, the S phase of the cell cycle is also the time when enormous amounts of histones are synthesized.

figure: Replication of telomeric DNA. Telomerase has a bound RNA molecule that is used as template to direct DNA synthesis and as extension of the ends of chromosomal DNA.