You do not have to create a new report server - if one of the source systems (or even the only source system) is upgraded or migrated. All you need to do is change the data source to point to the new system.
With that said - any time you are upgrading a source system you definitely need to test and evaluate all report code to ensure that new system doesn't break that code. If all of your report code is embedded in the RDL files, then you should build a test SSRS system and test every single report that uses that data source to validate it works as expected against the new system. If the code is contained in stored procedures on the source system - then make sure you test every single procedure after the upgrade/migration.
Of course - if the opportunity is available - you should consider upgrading your SSRS system to the latest available version if it isn't already.
Problems are opportunities brilliantly disguised as insurmountable obstacles.
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