Here is a picture of using telomerase in solving end replication problem (Courtesy: Molecular Biology of the Cell, Alberts, Garland Science Pub.)
Now lets consider the $3'$ end here, we are extending this end, and then using DNA Pol we extend the $5'$ end, even though the $5'$ end would still be truncated w.r.t $3'$ end but the original strand would be maintained. Now we know that this Telomerase enzyme is active in stem cells but NOT in somatic cells. So far so good.
Now if I consider the above layout in more detail: Lets consider what happens after the above replication cycle:
This is because in the 1st replication cycle, we have added more nucleotides to $3'$ end, as well as possible few more nucleotides to $5'$ end as well. Now this would create overhangs on each $3'$ end of my DNA. And I am confused on these overhangs. Either the replication machinery deletes these overhangs ( which I am not sure whether it happens), OR the second replication would start on these overhang DNAs. A possible issue with the second approach (i.e replication with overhangs intact) is that the length of each strand would keep on increasing with each replication cycle as we are keep adding new nucleotides to $3'$ end in every replication cycle!!
Can someone shed some light on how the second cycle would happen, and whether the overhangs would get deleted or it would remain (in this case strand length would keep on increasing)?