Sea Monsters

I would imagine it to look similar to a "Plesiosaurus" where it has a large stature, large fins, and a long neck. Possibly a blue color, or maybe three different cool color variants of lavender, sea foam green, and light blue. 
The basic purpose of the sea monster is to make the sea more dangerous (yes, we have the "Drowned", but those are just underwater zombies and the zombies became more of a nuisance than a threat long ago). The sea monsters could possibly travel in packs to defend the ocean, or maybe they only spawn in or around the sunken ships to protect their treasures. (I would think about 1-3 a pack if that direction were taken). The sea monsters could be attracted to shiny things, so if a player is wearing armor then the monster's heightened sight from being at the bottom of the ocean could spot the player more easily (if this is possible).

For drops, the sea monster could possibly give you a damaged trident, or possibly an already enchanted trident as it would be more difficult to farm the monsters than the drowned. The sea monster could also drop a form of sea flipper or scale which could be used for a special recipe, armor, or potion.

- Sea Monster Armor
     I would imagine that the sea monster's skin was pretty thick, so the armor penetration resistance could be heightened when it hits the water (so you lose more damage when wearing you're above ground then when you're underwater)

- Sea Monster Recipe 
   Maybe the sea monster flipper could be used in a soup to make a "sea flipper soup". This recipe can only be crafted by learning the flipper soup recipe obtained only in the sunken ship loot chests. The flipper soup, since it's very hard to craft, would either grant you a short status effect or a substantial amount of saturation and/or life hearts.

- Sea Monster Potion
   Since I'm leaning more towards receiving the flipper from the sea monster, I could see there being a special potion made with the flipper that makes you faster in water but slower on land, acting as if you have grown natural flippers.