Hello there, damirov_a.
The following Knowledge Base article provides some great information in regards to restoring your iOS device from a previous iCloud backup:
iCloud: Restore or set up your iOS device from iCloud
On your iOS device, go to Settings > General > Software Update. If a newer version of iOS is available, follow the onscreen instructions to download and install it.
Make sure you have a recent backup to restore from.
For information about backing up manually now, see Back up your iOS device to iCloud. If you don’t see a backup you expected to be there, see the Apple Support article If you need help restoring an iCloud backup.
On your iOS 8 device: Go to Settings > iCloud > Storage > Manage Storage, then tap a device listed under Backups to see the date and size of its latest backup.
On your iOS 7 device: Go to Settings > iCloud > Storage & Backup > Manage Storage, then tap a device listed under Backups to see the date and size of its latest backup.
Go to Settings > General > Reset, then tap “Erase all content and settings.”
In the Setup Assistant, proceed to “Set up your device,” tap Restore from a Backup, then sign in to iCloud.
Proceed to “Choose backup,” then choose from a list of available backups in iCloud.
For help deciding which backup to restore from, including information about restoring from another device’s backup, see the Apple Support article If you need help restoring an iCloud backup.
Additionally this article provides specifics on contacts in iCloud:
iCloud: iCloud storage and backup overview
Your iOS device backup only includes data and settings stored on your device.
It doesn’t include data already stored in iCloud, for example contacts, calendars, bookmarks, mail messages, notes, shared photo albums, iCloud Photo Library beta, My Photo Stream, and documents you save in iCloud using iOS apps and Mac apps.
Thanks for reaching out to Apple Support Communities.
Cheers,
Pedro.