Your external HDD can get infected in at least 3 ways:
Executable files stored on the ext. HDD can get infected, meaning that what they do when executed is changed.
Your ext. HDD can be made to boot a mini OS which then goes on to boot your normal OS. The infection for this can happen at any time though policies of your operating system can prevent unprivileged of doing the according changes. At least on Linux you should be fine as long as you don't give the malware root rights. Actually harming you, however, can only happen this way if your ext. HDD is connected while you boot your computer.
The firmware of your ext. HDD can be changed in such a way that it makes malware stored on it persistent. Then even overwriting your entire HDD doesn't get rid of the malware. This includes of course formatting existing partitions, deleting them, creating a new partition table, etc. Exploiting this requires vulnerability of your ext. HDD's firmware.
None of these ways of attack can be prevented by simply partitioning your ext. HDD into 4 partitions.
However, the first one can be partially prevented by partitioning your ext. HDD into 4 encrypted partitions and only decrypting the ones you're planning to use. If for example you only need access to the backups partition, only decrypt this one. Malware then can't infect your executable files stored on a different partition. If you want to transfer files from or to a computer which might have malware on it, only decrypt the file transfer partition. Make sure to never execute files from there.
Exploiting the second way of attack can as I already said be foiled by simply having your ext. HDD disconnected when you boot. If this is too inconvenient for you, maybe disabling booting from USB is a better option for you as this also renders this way of attack impractical. Make sure, though to not only change your boot order to put HDD first. Disable booting from USB all together in your BIOS settings. Otherwise malware which also uses the 3rd way of attack can trick your computer into booting from the ext. HDD anyways, however, it's very unlikely that this happens. I've never heard of a malware doing this.
The only ways the 3rd way of attack can be prevented is through OS policies or having an ext. HDD which makes in nearly infeasible to change its firmware. However, if you connect your HDD to a different computers, it might have different OS policies. And if that computer has a a malware with systems rights running, OS policies are useless.