If you're looking for a quest in Super Stories (they are timed quests from the past that you can relive through the Super Stories window), make sure that it is actually included in the game as a Story. You can find the list of Super Story quests Here in the help center

All quests in Supercity require players to be at a certain level in order to be able to start them. Make sure you meet the requirements for the quest you want to play.

Some quests are also locked until you complete the previous one in the quest chain. For example, this applies to the chain of Super Events: