The contract started on 1 July and the company will also undertake cleaning, caretaking and bulk removal at around 2,000 of Network Stadium's homes across north London.
The company has agreed to achieve high levels of customer satisfaction across the contract by the end of the first year and maintain or exceed them throughout the length of the contract.
It will also provide a mapping service of the client's "green assets" to identify open-space boundaries and the type of greenery on individual sites as well as surveying all trees.
Head of estate services Matthew Walker said: "We are confident that we will exceed the standards, which is our aim across all our existing contracts."
Network Stadium forms part of the larger Network Housing Group. Pinnacle also works with Willow Housing & Care, London Strategic Housing and Community Trust Housing.