The only pre-req is to have completed the other Thieves Guild quests (Darkness Returns, Imitation Amnesty, Silver Lining, Summerset Shadows, The Dainty Sload). After that "Under New Management" just consists of doing five jobs (probably your "mini-quest") in each hold. After you've completed 5 jobs in a hold, you are given a reputation quest with that hold. Complete one of those for every one of the four holds and Under New Management is completed.