gnomo223, you can link your 1TB drive to a location in your Home folder
Use the gnome-disks (search the main menu for "Disks") to find out where the 1TB disk is mounted. Let's assume it's mounted on /mnt/1TB
Now link the drive to a location on your Home
For example:
cd
or cd ~
to go to root of your Home
then
ln -s /mnt/1TB morespace
This will create a link morespace
on your Home storage (it can be any name you like, that is just an example)
Now if you change to the linked location, and list the files, you'll see the contents of the 1TB drive.
cd morespace
ls
You can also link individual folders on the 1TB drive to your home folder
An example: if you wanted to move your Music, Videos, or whatever, from Home to the 1TB, let's say Music.
Copy the Music folder to the 1TB disk
Delete the Music folder from your Home
Then link it back from the 1TB
ln -s /mnt/1TB/Music ~/Music
Your music player will continue to work as if the files had never been moved.
Check out Tutorials on linking files in Linux to get more understanding.
There's other ways to do it, like setting up LVM (Logical Volume Management), but not as straight forward).
Hope this will give you some idea.
Good luck!