Hi,
What is your backup tool? Windows Server Backup or other 3rd tools.
If you use WSB, you can configure another backup task and change the backup target from the old to the new partition. We cannot set two backup target in one backup task.

If you don't want to change the backup targrt location, you can extend your old backup target location to add the capacity for backup.
After extend the partition, you can use the "vssadmin resize shadowstorage"
to change the size for backup.
https://docs.microsoft.com/en-us/windows-server/administration/windows-commands/vssadmin
BTW, if you want to extend the partition, you should delete the unused partition and make sure the unallocated space is in the left of the partition.
https://social.technet.microsoft.com/Forums/en-US/01b0527e-4d1a-474e-8e6c-73a834b8f7ec/quotextend-volumequot-greyed-out?forum=winservergen
If you have anything unclear, please let me know.
Best Regards,
Daniel
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