General antonyms:
* Cause
* Permit
* Allow
* Encourage
* Promote
* Incite
* Bring about
* Provoke
* Induce
Specific antonyms depending on the context:
* Embrace (if averting means avoiding)
* Confront (if averting means avoiding)
* Accept (if averting means refusing)
* Invite (if averting means avoiding)
* Foster (if averting means preventing)
Example:
* Avert (avoid) disaster - Cause disaster.
* Avert (refuse) a request - Accept a request.
It's important to consider the specific situation and the meaning of "avert" in that context to choose the most accurate antonym.