If a Warframe update and PS4 firmware update are released within close proximity it is possible that your Warframe client will be unable to properly download and update until you have updated your PS4 console to the most recent Firmware version available.
On the function screen, select Settings (Settings) > [System Software Update].
Your system automatically checks if you have the latest version of the system software. If you do not, the latest update file is downloaded to the system.When the download is complete, a notification message is displayed in the upper left corner of the screen.
To install it, go to the function screen, select Notification (Notifications) > [Downloads], and then follow the screens to perform the installation.
Should Warframe still not start, please close the game and go to (Notifications) > [Downloads] and check for a failed /!\ Warframe update. Select the failed update and delete the file. The correct update should now be downloaded and installed automatically.
For alternative methods for updating your PS4 please visit the link below: