No. Light is a particle and it has finite speed, meaning its speed remains the same no matter what. That fact is not easily bent without breaking the laws of physics.
No Matter can travel at the speed faster than light. What I'm saying is that it is not light itself that is being expelled from quasar jets but matter that is emitting light. Cosmic matter made up of helium, carbon, hydrogen etc.. That jet you see from quasars is cosmic matter being expelled.
So considering the fact that matter cannot travel at the speed of light, it is safe to assume that matter expelled from quasar jets are not travelling at light speed or faster. Although it is very very fast that it is almost chasing the speed of the light particles it is emitting.
The speed of light particles emitted from cosmic matter in a quasar jet remains the same. There is no increase in velocity.
Here are links to clarify what I'm saying:
Can Matter Travel at Light Speed? | LiveScience
Superluminal motion - Wikipedia, the free encyclopedia