I bought a OEM Z tube for my 03 G Sedan, however I noticed
it's all Rubber and it's missing the clamps on both sides.

The metal part that goes around the tube, Both Sides.
I believe its the throttle connection, and the other side is the air filter box connection.

When I take off the Stock Tube can I use those connectors / clamps?

Thanks, Never done any of this stuff before.

I'm pretty sure u can use the clamps that are presently on ur car now.
It's plug n play.

Here's a DIY.
http://www.6mt.net/mod-g35-350z-intake.php

The one clamp from the G near the TB has a different set hole than the Z. I think the Z clamp has a triangle hole. You can use it, you just should cut off that piece of rubber sticking up and it will be fine.