You start out at the Royal Stable Master, as always...

Royal Stable Master says, "Think you can tame a Kelpie, then?"

Royal Stable Master says, "So let me get this straight. When you hear there's a [terrible beast] that drowns anyone who attempts to ride it, your first thought is 'that's the horse for me'."

Royal Stable Master says, "Well it's your funeral. Go see the old woman in Snowdonia Station. Amadra is her name. She knows the tales of beasts of Llyn Barfog, maybe she'll tell you one."

Amadra is up the stairs and to the right in Snowdonia Station.

Amadra says, "Well, Reaver, is it the Kelpie you are after? You'll find only misery. When I was a lass my friend saw a [mysterious horse] 'round here, and felt the need to take a ride. No sooner was he on the horse's back than it took off, straight in to the blue depths. We searched the shores many an hour, but nary a trace was found."

Amadra says, "Them beasts is nothing but malice on hooves, but capture one and you won't find a stronger steed. The key is in the [bridle]. Get the bridle off, and it'll be bound to you forever."

Amadra says, "Now to do that, you'll need to find a Kelpie and try to ride it. My sad tale comes from the shores of Llyn Barfog, and I suppose you'll be going that way too."

Go to Llyn Barfog and look for a mysterious horse. It'll be somewhere on the east coast, by the building. I found it at 40200, 33200. Interact with (right-click) the horse and you will mount it - and be unable to get off. The horse will run to the center of the nearby lake, you a captive, and then it will drop you into the water, transform into its true form, and attack you. The Kelpie is only orange con, so it's not a hard fight for a melee - some support classes and casters might have a problem, though. Have CC ready if you need range.

When you kill the Kelpie you will receive a Kelpie Bridle. /use the bridle while in the lake to receive the Kelpie.