Currently if you print a specific page it will keep the numbering, meaning that if the PageNumber in the viewer will be printed on the sheet as well (if you print page number 34 on the sheet it will be also 34). So this scenario is already covered by default.
If you have some requirement or a data set that has to be divided in groups, what you can do is reset the PageNumber on each new Report Group - you can find more information in that Reset PageNumber per Report Group
You can store the page numbers in your database using the code provided in the above blog post. Additionally with a few modifications you can just count the pages and record them to a database without resetting them.
In order to provide "print new pages" functionality you will have to compare the page count in your database with the page count of the rendered report; In this scenario however you must ensure that all the new information is at the bottom of the report - your queries have to be ordered by ID or by some other ascending numeric value. Any other sorting, grouping or querying without ORDER BY may move the new data to an "old" page. You also must have in mind that paging is specific for each rendering media - this means that depending on the media the page count would/can be different.
All the best,
the Telerik team
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