I can't open the picture. If it is just the spindle I brought a tap from Bunnings for $10 and just replaced the spindle the other day. Some taps unscrew from wall so whole tap can be replaced. If it is a soldered in tap and leaking from a joint a plumber job or someone that can solder. A rubber O ring can be worn in spindle allowing it to leak. They can be replaced but I just change whole spindle.
Buy a washer kit from plumbers supplies shop - linky Turn off your mains at the water meter Check that water is turned off (open the tap until pressure drops off). Unscrew top section of the tap Remove and replace washer Refix top section of tap & turn on mains Turn on taps in house & external to evacuate air.
And check the o ring while you are replacing the washer - as Shogun said. If replacing the washer/o ring doesn’t work, buy a new tap. You will need to use tape in the thread.
You should also check the washer seat and maybe give it a grind especially if the tap still leaks,, Just unscrewing and replacing the tap is probably the easiest and preferable to calling a plumber, just turn the mains of first,
It may be just a case of some thread seal tape on the connecting point with the garden hose,i can't see any leak on the tap..imho..
Grab a adjustable wrench, unscrew and screw a new tap on. Cheap as chips from Bunnings. As mentioned, use tape. My, that garden hose looks enticing with that green and gold piping. Front yard I take it?