Does buspar (buspirone) helps you improve quality of sleep?

Not neccesarily : It can make you drowsy which can lead to sleep . On the other hand if it is helping you with anxiety it can improve your sleep by controlling your mood disorder .

Buspar/ Buspirone: If a person tends to anxiously ruminate at night when they lie down- that can prevent sleep. Buspar (buspirone) can help to the calm mind so the brain can start to slow down in preparation for sleep. I often recommend a combination of Buspar (buspirone) and melatonin to people with this issue.

Buspar (buspirone) & sleep: Secondarily, when anxiety subsides.