If your game is linked to google play then when you reinstall the app it'll have you go through the sequence again of making a new sim, however when you enter the house it'll give you the option to restore your saved game or continue with a new game.
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This is a guide to saving your progress. If you delete the app without linking to an account you will lose your progress.
https://answers.ea.com/t5/Game-Information/Guide-How-to-save-your-game-progress-in-The-Sims-Mobile/td-p/6052342
http://forums.thesims.com/en_US/discussion/817478/hello-come-and-introduce-yourself
http://tinyurl.com/OneRoomOneWeek
http://tinyurl.com/rosemow
My Showcase thread https://forums.thesims.com/en_US/discussion/948861/rosemow-s-rooms-showcase