For a newer outside faucet leaking or dripping at the handle, it is probable the packing which can be graphite or an O-ring.
Remove the handle. Under the handle is the packing nut. Unscrew this nut to remove the stem from the housing.
There either an o-ring or graphite packing there that is the culprit. Replace it.
It is best to take it to the hardware store to be sure it is the correct one.
Put some silicone grease on the ring.
There is also a bibb washer. You might as well replace that, too.
Reassemble the faucet and apply some Teflon tape to the threads for a better seal.
If it still leaks, you may have to replace the entire faucet.