Welcome to Bunnings Workshop. That is a ball valve garden tap and is not worth repairing as the parts for it are custom. Anything more than ten years old and exposed to the elements has had a good run. I suggest getting a new tap as pictured below. Don't forget to put plumbers tape. You'll get another ten years hopefully.
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I agree with redracer01: your best bet would be to replace the tap. The product that they suggested would work a treat, but I noticed that you have a quarter-turn tap and thought you might like to keep that quarter-turn functionality. In that case I would recommend either an EnduraSeal quarter-turn tap with non-return valve or a Kinetic quarter-turn tap.
Something to keep in mind is that taps come in a couple of different sizes.
The easiest way to find the right size is to turn off the water supply, remove the installed tap, take it into your local Bunnings, and compare the size of your old tap to the size of the one you intend to purchase.
Once you get home, make sure the threads inside the pipe are free of debris, wrap some PTFE tape clockwise around the threads on the tap approximately 6 times (make sure the tape does not block the hole), and screw in the new tap. You can then turn the water back on and check that the new tap is not leaking. If it is, tighten the tap another turn until it is no longer leaking.
Good luck with it