Have you considered a pump? We have one for our water tank so we can use the water across the garden. Without the pump we could only really use a soaker hose.
Thanks @Jason for the advise. I assume these are the ones https://www.bunnings.com.au/our-range/bathroom-plumbing/plumbing/pumps/constant-pressure-pumps
What pump have you got?
Regarding low water pressure, and initial cause of leaking gate valve:
Have you checked for debris inside the tank, ? gate valves don't do well with debris, it gets jammed under the gate. and there maybe leaves/ sticks/ silt/ frog blocking the pump outlet.
If you connect a hose up to your tank (using the arrangement you have just made), then you should be able to force any blockage back into the tank. If this improves the flow then you will need to clean the inside of your tank at some stage.
Using some 19mm poly pipe will double the flow compared to a standard hose.
It looks like the water is bypassing the packing ring around the stem. Most gate valves have a packing ring around the stem to stop the fluid leaking up the stem and as the nut just below the handle is tightened the packing is compressed to create a type of O ring effect you may be able to replace the packing ring. failing that replace the valve