All 12 Uses of

cleave
in
The Return of the King

In each hand he held up one half of a great horn cloven through the middle: a wild-ox horn bound with silver.†
Chpt 5.1 *

cloven = split (or divided in two)

Flats and meads of rough grass, grey now in the falling night, lay all about, but in front on the far side of the dale Merry saw a frowning wall, a last outlier of the great roots of the Starkhorn, cloven by the river in ages past.†
Chpt 5.3

Drawing his eyes down from the tower and the horns of the Cleft before him, he forced his unwilling feet to obey him, and slowly, listening with all his ears, peering into the dense shadows of the rocks beside the way, he retraced his steps, past the place where Frodo fell, and still the stench of Shelob lingered, and then on and up, until he stood again in the very cleft where he had put on the Ring and seen Shagrat's company go by.†
Chpt 6.1

Then suddenly he realized that it was not so, his hearing had deceived him: the orc-cries came from the tower, whose topmost horn was now right above him, on the left hand of the Cleft.†
Chpt 6.1

Out of a gully on the left, so sharp and narrow that it looked as if the black cliff had been cloven by some huge axe, water came dripping down: the last remains, maybe, of some sweet rain gathered from sunlit seas, but ill-fated to fall at last upon the walls of the Black Land and wander fruitless down into the dust.†
Chpt 6.2

cloven = split (or divided in two)

But only a short way ahead its floor and the walls on either side were cloven by a great fissure, out of which the red glare came, now leaping up, now dying down into darkness; and all the while far below there was a rumour and a trouble as of great engines throbbing and labouring.†
Chpt 6.3

cloven = split (or divided in two)

All day far below them a leaping stream had run down from the high pass behind, cleaving its narrow way between pine-clad walls; and now through a stony gate it flowed out and passed into a wider vale.†
Chpt 5.3

No other blade, not though mightier hands had wielded it, would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.†
Chpt 5.6

Uses with a meaning too rare to warrant foucs:

Fewer were they but they clove through the Southrons like a fire-bolt in a forest.†
Chpt 5.6

clove = a dried flower bud or section of a garlic plant

The outstretched neck she clove asunder, and the hewn head fell like a stone.†
Chpt 5.6 *

Definitions:

(1) (cleave as in: cleave through)
to split or cut through something

Ironically, this word can mean to split in two or to hold together.

Note that you may see cleaved, cleft, clove, or cloven as the past tense of this sense of cleave.
(2) (cleave as in: cleave to)
to hold firmly to something -- such as an object, a person or idea

Ironically, this word can mean to split in two or to hold together.

Note that you may see cleaved, clove, or clave as the past tense of this sense of cleave.
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

a proper noun or other word too rare to warrant focus