If the new drive is big enough for all Bitcoin data: Maybe. Just reconfigure Bitcoin’s data folder and copy contents across (not necessarily in that order!)
If you are thinking two drives together will provide for Bitcoin’s needs: No. I think it probably isn’t simple to split the storage of Bitcoin-core’s data directories across two drives. In principle you could, for example, make .../blocks/ a mount-point for the second drive, but I wouldn’t advise this.
2.0. make a backup of any wallets and test that they can be restored successfully.
2.1. stop Bitcoind
2.2. cd {wherever Bitcoin data directory is configured}
2.3. sudo mv blocks oldblocks
2.4. sudo mkdir blocks and fix permissions, ownership etc
2.5. mount the partition of the second drive at this new blocks folder
2.6. something not entirely unlike cp -p oldblocks/* blocks/ (you should definitely test this on small test data folders first).
2.7. cross fingers and restart bitcoind
I have not done the above and just made it up off the top of my head. Caveat emptor. I much prefer just replacing the 1TB drive with a 2TB drive – much less risk.
