If you're talking about reducing pain or stress:
* Relief: This is the most direct noun form of "relieve".
* Ease: This suggests a gradual lessening of discomfort.
* Comfort: This implies a feeling of being soothed and relaxed.
If you're talking about replacing someone in a job:
* Replacement: This is a direct noun equivalent.
* Substitute: This emphasizes the temporary nature of the change.
* Relief: This is also used in this context, particularly for military personnel.
If you're talking about the act of releasing someone from duty:
* Discharge: This implies the formal ending of someone's responsibility.
* Release: This can refer to being freed from captivity or duty.
Other possibilities:
* Mitigation: This implies reducing the severity of something.
* Alleviation: This suggests making something less burdensome.
The best noun for "relieve" will depend on the specific context and the nuance you want to convey.