My car vibrates on the bite point when no gas is given only at first gear (manual transmission). When gas is given it works fine. IT IS A NEW CLUTCH.
If your old clutch was replaced because it was worn out (or nearly worn out) then the new clutch is likely to be providing a significantly higher amount of friction at the biting point than the old one has for quite some time (similar to how new brakes will be able to stop the car much more sharply then heavily worn ones). The energy the engine is providing is insufficient to overcome this friction but it has to go somewhere - hence the vibration.
When you give it more throttle you are allowing the engine to overcome this friction (and the car then drives off).
So in other words (as Steve's excellent answer points out) this is normal behavior and nothing to worry about.
By not giving the car any throttle and with a fresh new clutch installed, you are attempting to induce a stall. This behaviour is by design. If you are very very gentle and the car is fuel injected, the ISV might eventually catch up and you may be able to move off without any throttle.
This is poor driving technique as you are effectively "lugging" the engine. You'll experience the same type of effects as driving up a hill in too high a gear. You should apply an amount of throttle before (and as) you release the clutch.