Currently using a dual boot system with windows on one drive and KDE Neon (Ubuntu 18.04 LTS + latest KDE) on another, I have had Grub installed when I installed Linux the first time.

Now purchased a new NVMe SSD I will migrate my whole C drive with Windows installation and where Grub lie.

I expect Grub will be not maintained during the disk migration where I will use Paragon Drive Copy to clone the old Windows installation into the new disk.

Need I to "reinstall" grub? Since I didn't installed it in the first place Im not sure how to manage this.

Ubuntu has great doco, especially on handling grub issues.
But you might get lucky - if not it should simply be a matter of chroot-ing into your system and running grub-install followed by update-grub.

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There's also Grub Rescue, contained in this disk.

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What I didn't understand is if being my grub installed in a different disk from the Linux installation need to be managed in a different way.

You don't indicate which version of windows you are using or whether you are using UEFI to boot. The default install of Ubuntu on an EFI machine is to install the Grub efi files to the first EFI partition it finds and if you have windows 10, Grub EFI files are likely on the windows drive on its EFI partition in an ubuntu directory. Running sudo fdisk -l and/or sudo parted -l will show where your EFI partition(s) are. Mounting them will show where the ubuntu EFI files are.

If your system is uefi it is hard to say, not all uefi firmware/bios are created equal.

Tested today just adding the new disk (with no formatting, no disk migration, nothing) and Windows boot is generating an error and need a reboot.
Removing the disk all is back to normality.
I suppose something need to be changed in grub since Linux boot is working fine.
Tomorrow will check about UEFI boot status.

Or not.
That indicates that the firmware is enumerating the new drive first, and all the EFI variables in the NVRAM are pointing to addresses on that new (empty) drive. Nothing to do with grub as the firmware can't even find it. No idea on your Paragon software, but for Linux, just chroot into your system and grub-install to the new drive - it updates those (Linux relevant) variables for you. Best to get Windoze copied over first I would think.

Ok In Linux first formatted in NTFS the new drive and next performed grub-install and next boot-repair, got the same error rebooting in Windows.
Digging a bit more resulted that might be a drivers problem so trying to boot in safe mode I was able to boot in Windows.
Uninstalled Nvidia drivers using Display Driver Uninstaller and I was able to boot normally in Windows.
Uninstalled physically Nvidia GPU for safety and now working only with the primary AMD one, working on the sda drive clone using Paragon Drive Copy, will see how is coming out.