I had exactly the same issue:. Synology DS213 with a 3 TB hard drive. I was adding another harddrive of at least 3 TB. Raid of type SHR (Hybrid)It is now very easy to add the drive (I have DSM 6.0.2 for what it matters).
Go to Storage Manager Volume. Click on Manage. Select Expand size (I know, this is very misleading). Select the new hard drive. Wait until the operation finishes: you can now see 'with data protection of 1 disk fault-tolerance)Note: you need to have at least the same size on the new drive and it's better to have similar model.Cheers. I have Synology DS414, the 4-bay NAS with two 1TB disks installed and configured as one volume via SHR (Synology Hybrid RAID).
Today I received two more 8TB drives. Here is what I did. First of all DS414 supports hot-swapping, meaning I can add drives without turning off the NAS.
Having said that I installed one 8TB drive. Waited, nothing changed. I can't see the drive in Storage Manager, and the 'Manage' button is disabled. Very scared. Decided to restart NAS. After reboot = go to Storage Manager. Now I see the 'Manage' button is enabled.
Click on it and I see the 'Choose an action' popup. I choose 'Expand the volume by adding hard disks'. This is what I want, though there are other options. In the next step it asks to 'Choose disks'.
I choose the new drive which shows 7.28TB for its disk size. Click 'Next'. Click 'Apply'. Now NAS starts expanding the volume by adding the new disk. But this process takes very long time, at least for my 8TB. It's been 24 minutes, and the process is only at 1.77% checking parity consistency.I followed this help article from Synology.