Your Stats and Best Time are saved locally on an iOS device and cannot be transferred over.
When the app is deleted or reinstalled, the stats will reset.
The same is true when playing on multiple devices, despite being logged into the same Apple ID and Game Center account.  If you reset your stats on one device, it will not reset on the other.

Achievements and Leaderboard scores can be backed up and restored.
Below are Apple Support articles to backup and restore your devices:
Apple Support Article: How to backup your iOS device
If you were using Game Center on your old iOS device, you will be able to log in with your Apple ID on your new iOS device and continue to update your Score and Best Times.
To sign into Game Center:
  1. Navigate to your device's Home Screen
  2. Select the Settings App (gray gear icon)
  3. Scroll down until you see Game Center
  4. Sign into this page using your Apple ID
  5. Return to Solitaire and access your scoring information in the Menu bar under Game > Stats
Please note: if you are switching from an Android to an iOS device, or vice versa, scoring information is non-transferrable. We apologize for any inconvenience.
iOS (iPhone, iPad, iPod) --> Android (mobile, tablet)
Android (mobile, tablet) --> iOS (iPhone, iPad, iPod)
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