This page in our guide to Control will tell you whether you can continue playing the game after completing the story.
Can you play after completing the story?
The answer is yes, you can keep playing after completing the story. You can perform remaining side quests, hunt bosses, or collect trophies/achievements. Nothing prevents you from repeating some main missions from the game menu. In Control, you will find a lot of extra content - the game has a lot of hidden side missions, a few challenging boss fights, or secrets to discover.
After completing the plot, you unlock the Director's costume, and Jesse will get some extra dialogue lines when you return to previously visited locations. Moreover, there are a lot of new notes to pick up, and the developers have already announced two DLCs that will flesh out the game's universe - AWE and Foundation. Everything indicates that this is only the beginning for the heroine and further adventures, and the potential sequel is very probable.