It depends. Some apps store data on their own server in which case you would have to ask the developer. In most such cases, the game would have an account that you sign into, in which case signing in with that account within the app should restore your saved progress. The other possibility is that it stores data locally on the device, in which case if you make an iCloud backup, signing into your Apple ID and restoring from that backup on another device should retain your saved data.
Keep in mind that getting a new device is a big step if the only issue is that the game is crashing. There are other troubleshooting steps to try first, including reinstalling the app. Also check reviews in the App Store to see if other people have the same issue, the developer may need to issue a fix.