You can get deeper trellis perhaps? but will it put more load/stress on your existing fence which may become unstable in gales.
Before spending more money/time etc, dont forget most back and side gardens fences have a height restriction of 2 meters max and it sounds as if you are already well over this? If you push it any higher you may have to remove it down to 2 meters?
One way some increase their privacy is to put a tree or a trellis nearer the house?

The top of the trellis is currently 8-9 feet from the ground.

The fence backs onto an alleyway and is away from the main road.

I removed the trees that were in front of the fence coz I wanna build something in that area.

What can I do above the trellis for privacy?

JH

I suspect it would not be legal or safe to add more to this already high structure? Is the fence and posts in good order as they are already supporting a lot of heavy trellis?
If the alley way is used and someone considers what you do to the height is dangerous or even threatening you could make costly trouble for yourself? If you building a structure something over 2 meters and permanent you may need planning permission first?
Why not ring your local council/planning department and see if they have any suggestions as to what you can do to solve your problems, if they would allow a pitched roof on your new structure that might solve the privacy problem?

If it was just greenery on the trellis that extended higher, would that still constitute building something too high?

In theory yes, but I think if you grew plants on the 8-9 feet trellis you already have in place, you will get away with the height, because no one will notice the difference? But if you go even higher with wooden trellis that you may find someone complains how dark and forbidding the alley way has become.
Nothing really will grow much higher than the trellis as it will bend over without support. But 8-9feet of climbers could be very dense and could do a good job for you

I didn't really want the bottom part of the fence covered with anything.

I just wanted something that's sturdy and can sit on the trellis projecting upwards so gives me the amount of privacy that I need.

Hope you solve your problem

Something like a plastic barrier in green would give some privacy. You would need to attach and screw it into the fence and therefore makesure that the fence is strong enough. I have seen them used for privacy all over the world. To give you an idea what I mean:

http://www.gltc.co.uk/fcp/product/-/parenting%20magazines/High-Visibility-Driveway-Barrier/657

Where you source it in the UK I do not know.