As the iPad has limited power capabilities, dependent upon the Storage Device, an external power source is often required. For HDD or SSD, connected via USB, an external power source is almost certainly required.
If you have one of the newest iPad Pro models, with a USB-C connector, you may need to utilise a powered USB hub (i.e., it has its own source of power) - connecting both the iPad Pro and the storage device to ports on the hub - or an Apple USB-C Digital AV Multiport Adapter:
https://store.apple.com/xc/product/MUF82ZM/A
There are many third-party USB Hubs that have a USB-C connection for iPad plus a USB-C PD (Power Delivery) pass-through power connector to which you can connect your USB-C Power Adapter - along with the hub itself incorporating a combination of additional USB-C ports, USB 2.0/3.1 Type-A ports, Ethernet LAN, HDMI, VGA, SD and microSD card-readers. Perhaps consider Kingston, Anker, Hyperdrive and Satechi - although there are many others from which to choose. A Google Search for USB-C Hubs compatible with iPad will find a number of articles and recommendations.
Some additional information about connecting external storage devices can be found here:
Connect external devices or servers with Files on iPhone - Apple Support
https://www.imore.com/how-use-external-hard-drives-your-iphone-or-ipad
To be recognised by iPadOS, the attached USB storage device must be formatted to FAT, FAT32, exFAT, APFS or HFS+ with a single partition. Microsoft NTFS is not supported. Formatting and partitioning, if required, must be performed using a separate computer; iPad does not provide any facilities to format an external storage device.
When choosing an SSD for use with iPad, you will need to avoid any that include hardware encryption that are reliant upon installation of software drivers. iPadOS provides no facility for device-specific driver installation beyond those incorporated within an installable App.