We would need a bit more detail here.
You need to have an account on the Frontier Store Site as well as the Steam Purchase. It uses your email address to log in.
Go to this site and register using the same email address you have for Steam.
The Frontier Developments Online Store is the exclusive online retailer for products made and licensed by Frontier Developments plc
www.frontierstore.net
Then login to your account at the above website and look for "Steam Entitlements". You should see the entitlement for Steam.
Also, while logged into your Frontier Account, look for "Third Party Accounts" and "Link" your Steam account to your Frontier Account.
Then when you launch the game, in the "Launcher", enter the "email address" and the "password" you chose when creating the Frontier Store Account.
You should be able to play if you have successfully completed these steps.