"Contract: Missing Brother" is a side quest in The Witcher 3: Wild Hunt.

This is one of the contracts you can pick up early in the game during The Nilfgaard Connection, from the notice board just outside the "Inn at the Crossroads". This side quest however has a suggested level of 33, so it is highly unlikely you'll be able to do it then, and will only be able to do it near the end of the game.

After getting the contract from the notice board, talk to Bruno just inside the Inn.

Talking to Bruno you can convince him to increase your reward by up to 44 crowns.

Head to the map marker for where the mine is. Just outside the mine, use witcher senses to examine the dead body, and monster tracks leading inside the mine. Keep following the tracks and you'll eventually come across some monster eggs that will hatch soon. This'll open up an optional objective for this quest, which is use witcher signs to destroy all eggs. It's an optional task that will get you some more experience points -- so look for the Monster Nest icons while you go exploring to find them all. There are three areas, with four nests/eggs each. You can reach the areas by diving through underwater tunnels.

When you encounter a blood stain which can be examined, Geralt determines that it's an Arachas monster. If you wish to do the optional objective you'll need to do so before encounter the boss, or this objective becomes uncompleted. The name of this Arachas is Harrisi. It likes dropping poisonous clouds arround itself.

After dealing with the arachas, loot the corpse, and return to Bruno to collect your reward.