Old guy here who still has a couple G4s and remembers when. Some things to check:
It depends on your Leopard DVD. Only the retail version should work to install on a G4. If that's not what you have (a restore disk for a different Mac, for example), it may not work. I have that retail disk image if needed.
The drive needs to be a DVD-DL and many G4s do not have that. I don't believe it was OE till the dual-core versions around the time that the G5 was released.
Like all PPCs, a G4 will not boot from a USB external—it can read from one but not boot. You can try selecting it as a startup disk from the G4 but holding down the C key won't cut it. The drive needs to be internal or FireWire to boot.
There are ways to load the disk image onto your hard drive and install from it but it's been 12 or more years since I did that.
Now here's the kicker: Many G4s cannot run Leopard at all (my 700) because the GPU is incompatible, even if you get it installed (there's a hack or you install it on a later G4 and move the HDD over). An 800 is the minimum. Or it runs so slow, it's not worth the effort like my dual core 1G—I threw in the towel on that machine. Both of mine now dual-boot into OS 9.2 / OS 10.4.11.
I intend to install an 128GB SSD into my twin-core this summer. I bought an ATA to SATA adapter that's supposed to work. We'll see... It won't see larger than 120GB so I'll try partitioning into 3. Will try OS 10.5 again just to see what happens.
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The old drive is now working in another PowerPC. I could target boot the other PowerPC and connect the one with the new disk through firewire and select the other disk as boot device. I don't know how that works.
If a DVD-DL drive, that should work. You may have to run Disk Utility to format the drive, however which will wipe the drive.
If it asks to
Update the drivers, that's ok and will not erase the drive.