Hello Susan,
Thanks for using Apple Support Communities.
From your post I understand that you gave your old iPhone to your child, and after they deleted contacts from it, they also deleted from your iPhone. This indicates your child's iPhone was signed in to your iCloud account, thus keeping all of the content between them in sync.
To get your contacts back, you will need to restore from your most recent backup. In order to avoid this situation in the future, sign out of iCloud on your child's iPhone.
Restore your device from an iCloud or iTunes backup - Apple Support
- Tap Settings > iCloud on your iOS device. If you see the option to sign in, you can change your Apple ID now.
- Scroll down and tap Sign Out. In iOS 7 or earlier, tap Delete Account. After you sign out of iCloud, you might not be able to access some of your data that's stored in iCloud until you sign in again. If you're part of a family, you'll need to sign back in to use Family Sharing.
- Choose Keep on My iPhone or Delete from My iPhone.
- Enter your password.
- Go to Settings > iCloud and enter your Apple ID and password.
- Tap Sign In.
Sign in with a different Apple ID on your iPhone, iPad, or iPod touch - Apple Support
Take care,
Alex H.