Why don't I have the gallery??

Do you have an under age account? If so that is why.

IF the issue is not that you have an underage account...

• Is your "Enable Online Access" option checked in the Game Options panel? If not, check it then see if the Gallery appears. You may need to log off/exit the game and Origin to see full effects.
• If "Enable Online Access" option is not available/greyed out and not allowing you to check it, you can try adding Origin to the whitelist/exceptions on your computer's firewall &/or antivirus.
• You can try to 'repair' your game. 
• You can try saving a copy of your current game file onto your computer in a different area (or preferably an external drive). If you have a backup you can roll back to a date/version without the issue and not completely lose your game. Go to Documents > Electronic Arts > The Sims 4. Right click on the file "The Sims 4", copy it. This file is your backup of your game saves, etc. You should save a copy of this folder occasionally in case your game or computer crashes. Save it to an external drive. That way you could add this folder into a fresh install and recover your lost game should you need to.
• Then... you can try a fresh install of the game and replace the "The Sims 4" file in the new install with the one that you saved from your current game.

Good luck!