You could probably come up with something homebrewed relatively easily, such as (off the top of my head):Level 1: Gain bite attack doing 1d6+STR, plus Martial Weapon proficiency. Bite Attack usable as a Bonus Action WISMOD times per day.
Level 2: Channel Divinity: Sets one tasty-looking enemy as target of your gluttonous hunger for 1 min. Each time you deal damage to that target, you gain dice worth of HP or maybe Temp HP. If you hit with your bite attack, you gain additional WISMOD HP/Temp HP. Increase the dice at higher levels?
Level 6: You can use your Channel Divinity to inflict debilitating hunger on any creatures of your choice that you can see within a 30 foot radius. They must make a CON saving throw or suffer dice+level (or dice increasing with level) worth of poison/necrotic damage and 2 levels of Exhaustion. A successful saving throw halves the damage and they only suffer 1 level of Exhaustion. Constructs are immune (to the Exhaustion at least), since they don't/can't get hungry.
Level 8: Divine Strike: Each weapon attack does +1d8 Necrotic damage, increasing to +2d8 at Level 14.
Level 17: ???? Some ability to to turn you into a ravening whirling dervish of biting and chewing. (Seriously... who plays Tier 4?)
Domain Spells:
1: Goodberry, Inflict Wounds
2: Locate Animals or Plants, Ray of Enfeeblement
3: Hunger of Hadar, Create Food and Water
4: Blight, Sickening Radiance
5: Contagion, Enervation
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