If your Mac has no read or write access to the new drive, you ought to check if the drive is formatted to a Mac-compatible file system. If not, go to Disk Utility and format it to HFS, HFS+, or APFS file system right at this moment.
Here is the detailed step: How to Format (External) Hard Drive for Mac and PC? A Stepwise Guide
If you would like to use this hard drive on both Mac and Windows, keep it NTFS-formatted and install iBoysoft NTFS for Mac on the macOS device, so the drive will be mounted in read & write mode automatically once it is connected to Mac, and you can read and write it with ease.