Upgrading an SSD drive in a Late 2013 Mac Pro

What do you mean by "to up grade add on to 1TB external drive "?

With an adopter one can use a "standard" NVMe blade SSD in place of the Apple blade SSD. But there are problems with some. See:

970 evo mac pro - Apple Community

OWC also sells replace blades SSD

https://eshop.macsales.com/shop/ssd/owc/mac-pro/2013

The Mac Pro 2013 supports external drives via USB. These could be USB 1.0, 2.0 or 3.0 all of which use the USB-A connector. It can also use USB 3.1 drives which have a USB-C connector but here you would need a USB-A to USB-C cable.

The Mac Pro 2013 can also use Thunderbolt external drives. Thunderbolt 1 and Thunderbolt 2 drives would simply plugin, Thunderbolt 3 drives would require you to also buy an Apple Thunderbolt 3 to Thunderbolt 2 adapter.

The Mac Pro 2013 when running the Mac operating system can read, write and format drives as Mac Extended aka HFS+, Windows FAT32 and ExFAT. The Mac can as standard read but not write or format drives as NTFS. The Mac as standard cannot read, write or format drives as EXT3 or EXT4. (As used by Linux.) It is possible to get software for the Mac to allow it to fully use NTFS or EXT3/EXT4 but this would cost extra.

If you actually really meant how to replace the internal 500GB SSD drive with a new 1TB internal SSD drive then this is possible.

1. You could try and find a secondhand genuine Apple SSD as used either in another Mac Pro 2013, or a MacBook Pro 2013-2015 or an iMac from 2015. The SSD slot inside the Mac Pro 2013 uses Apple's proprietary connector which has the notch in a slightly different position to a normal M2 style SSD drive
2. You could buy an SSD drive from OWC, they make and sell ones specifically designed to match Apple's proprietary connector
3. You could buy a standard M2 SSD and get an adapter card which adapts/converts it to Apple proprietary connector, see - https://www.amazon.com/Sintech-Adapter-Upgrade-2013-2015-MacBook/dp/B01CWWAENG/

Note: There are a number of such adapters around, check the small print carefully to make sure it works in a Mac Pro 2013 and that it supports the SSD drive you want to use. For the above one I did see a 'feedback' saying someone had used it in a Mac Pro 2013 successfully.

Note: Originally the Mac Pro 2013 (and classic Mac Pro models) only supported booting from AHCI style internal SSD drives. Apple have added support for booting from NMVe SSD drives with a firmware update included in Mojave when you install Mojave on a Mac Pro. This is a huge plus as Samsung for example no longer make and sell AHCI style M2 SSD drives. AHCI and NVMe drives use the same physical connector.

Note: The original Apple SSD drive comes with a heatsink. Many replacement SSD drives do not. For a Mac Pro 2013 you do ideally want to fit a heatsink as if the SSD gets too hot it will both slow down significantly (to reduce heat) and potentially reduce the lifespan of the SSD drive. See - https://www.amazon.com/EKWB-EK-M-2-NVMe-Heatsink-Black/dp/B073RHHYCM as some examples

well, if it's an external drive, just plug it in, if it's Mac formatted, it should be recognized and show up on your desktop. If you need to format it, Disk Utility should be able to do that for you. If you want to upgrade your internal SSD to 1 TB, here's a webpage that might get you started

https://eshop.macsales.com/shop/ssd/owc/mac-pro/2013?ds_rl=1242044&ds_rl=1242044&gclid=EAIaIQobChMIq_rdkMjy3wIVUxx9Ch0j7AHaEAAYASAAEgJ5tvD_BwE&gclsrc=aw.ds

oh and you might want to do a backup first....you do have a backup system in place, right??

John B