[put|set] {one's} [mind] at (rest|ease)

to assure someone that they no longer need to worry about a particular person or thing

The origin of the idiom "put one's mind at rest" can be traced to the concept of achieving mental calm and tranquility. The phrase draws upon the idea that when someone's mind is troubled or restless due to worries or anxieties, there is a need to address those concerns and provide reassurance.

The doctor's explanation about the test results put her mind at rest, alleviating her worries about her health.
After confirming the safety measures in place, the anxious traveler's mind was put at ease, allowing them to enjoy their trip.
Receiving an apology from her friend helped set her mind at rest and restored their friendship.
The thorough inspection of the house put the buyer's mind at rest, assuring them of its structural integrity.
The teacher's clarification about the exam format put the students' minds at ease, easing their anxieties and allowing them to focus on studying.