Skyrim thieves guild 4 special quest done

I have finished all 4 special quests for Delvin but I'm not becoming the Guild Master. I am playing it on PS4 and version 1.07

The four special quests, triggered by doing the radiant quests from Vex and Delvin, are not the quests to become the guild master.

The main quests for the Thieves' Guild are as follows:

• A Chance Arrangement
• Taking Care of Business
• Loud and Clear
• Dampened Spirits
• Scoundrel's Folly
• Speaking With Silence
• Hard Answers
• The Pursuit
• Trinity Restored
• Blindsighted
• Darkness Returns
• Under New Management

The 4 special quests are important for restoring the Thieves' Guild's status in Skyrim. Good Start.

The Guild's Main Quest-line (as delineated in Nelson's answer) is how you deal with the fact that, as Delvin Mallory so quaintly puts it, "Somethin' out there is piss-drunk mad at us."

Once you have dealt with both of these issues, you can become Guild Master.