Can't write to Seagate external hard drive on other macbook pros
If the drive is NTFS the MacOS default driver is read/only. 

You probably have installed a driver at one time on your old system that provide read/write. 

Such a driver frequently come with external harddisks. I have personally found this preloaded on recently purchased Seagate drives formatted as NTFS, but that only supported Seagate drives.  Paragon sells the full driver from https://www.paragon-software.com/home/ntfs-mac/ (they also have for other filesystems).