http://www.guru3d.com/articles-pages/asus-radeon-r9-380-strix-review,5.html
Here they tested the power consumption of a R9 380 with an overclocked i7 5960X and found the entire system pulled under 350w (from the wall, which means even less on the PSU output side). They also estimate the GPU itself to be puling around 190w, or around 11amps. The Antev VP450 has 18 amps available on the rail that powers the GPU, it also shares that rail with the HDD motor, (molex) fans, optical drive etc. But there's no way all those are going to pull the other 7 amps.
And according to tests by Hardwaresecrets they actually managed to pull 22amps per rail in the overload test before the protection circuits shut it down.
http://www.hardwaresecrets.com/antec-vp450-power-supply-review/
I think you can actually use your current PSU and be fine. But you will be cutting it a little close.