Hi, and welcome!
While Windows and Zorin OS use different file systems – NTFS and EXT4, respectively – you don't normally need to re-format; Linux can read drives formatted with NTFS.
Something that tends to cause trouble are spaces in the name of the drive e.g "Seagate Expansion Drive". You can change the name of the drive by launching "Disks" from the application menu, selecting the external drive and use the cog icon on the left-hand side to edit it. The name doesn't matter, it should be something that you can easily identify, maybe just replace spaces with underscores e.g. "seagate_expansion_drive" for example.
I don't have Zorin OS right now and I don't remember how this looks like exactly, but should be somewhere over there. If you are not sure, just give it some more time until someone else can give a more accurate reply on this one.
You can also give this thread a read to have a better idea of how to use "Disks", what options are available and how you can specify whatever folder you want to use to mount the drive. Normally this is not necessary, but just in case this interests you: