How is the external drive currently formatted?
Control click on it’s icon and select Get Info
macOS can not write to a windows NTFS formatted external drive without using special software.
You can store music files and albums on a FAT-32 or eX-FAT formatted drive to share with both macOS and Windows.
If you want to move your entire music library intact, then the external drive needs to be formatted for macOS.
see > Erase and reformat a storage device in Disk Utility on Mac - Apple Support
Caution: reformatting the external drive, will erase all of data that is currently stored on it.