Exterminator

The life of an Exterminator is sometimes quite violent and aggressive but can also be calm, collected and wise. Some Exterminators may seem like Barbarians when they see their favored enemies, while others may act more akin to Druids or Bards. The Exterminator is extremely specialized in fighting and dealing with it’s favored enemies. The Exterminator’s goal may be to contain, aid or eradicate a certain  type of enemy. 

Predictable Foes

At level 3: 
You may add double your WIS modifier to any CHA checks involving your favored enemies in place of your CHA modifier. You also gain advantage on all Insight rolls. 

Adjusted Technique

At level 7: 

Pick one of your favored enemies (or 2 humanoids), you have advantage on all attack rolls against them and they have disadvantage against any saves they make against your spells or grapples. 

Mental Study

At level 7:
As a bonus action, you can roll a d20 for the following effects: 

1-5: You know the CR of the monster 

6-10: You know the CR, attacks, bonus effects and attack damages of the monster 

11-15: You know all the above along with the Vulnerabilities, Resistances and Immunities of the monster 

16-20: You know all the above and the average HP and ability score modifiers 

You can use this feature only once per combat and only an amount of times equal to your WIS modifier per long rest. 

Learned Tells

At level 11:
When one of your favored enemies attacks you, they attack with disadvantage and you also have advantage on spells and similar effects that were caused by your favored enemies. 

Enemy Weak Points

At level 15: 
Choose one of your favored enemies, on each attack that hits, you may choose to either get a critical hit or to do get the maximum roll possible, however if you roll a critical hit and choose to get the maximum roll, you lose the extra dice from the critical hit. This does not apply to spell damage. 

Favored Spell

At level 15: 
Pick a single spell of 4th level or lower that is related to one of your favored enemies, this spell does not count as one of your spells known and can be cast a number of times equal to your WIS modifier. 
Some suggestions:

Beasts: Dominate Beast 

Construct: Heat Metal

Elemental: Elemental Bane 

Fey: Summon Fey 

Plant: Blight 

Etc.