"undertaking development" is correct and usable in written English.
You can use it in many contexts, but most typically in business and academic contexts to mean "taking on a development project or task". For example, "The company is undertaking development of a new product line."
In the late 1960s Rolls-Royce undertook development of a new, powerful jet engine, the RB211.
Slap the label of "humanitarian crisis" on a situation and it becomes difficult to undertake development work.
Each year, international financial institutions (IFIs) provide governments and companies billions of dollars to undertake development projects.
Auburn University awarded a subcontract to Foster-Miller, Inc. to undertake development of the 5 kW Stirling convertor assembly.
The agreement announced Sunday calls for the government to distribute land to small farmers and undertake development projects that would improve education and infrastructure, among other measures.
Researchers at the Idaho National Engineering and Environmental Laboratory and Montana State University have undertaken development of MINERVA, a patient-centric, multi-modal, radiation treatment planning system.
"This makes it more difficult to undertake development work, to respond quickly and flexibly to initiatives and to maintain the standard and extent of service provision," he said, in the 2016/2017 annual report.
With Nintendo failing to undertake development of a new adventure through labyrinthine caverns riddled with secret paths and battles against bloodthirsty space pirates, Metroid devotees were left pining for something new.
He later moved to the Mugello Circuit with Barrichello performing engine and setup testing, while Ferrari's test driver Luca Badoer remained at Fiorano and undertook development work for new car components.
The research team undertook development work in one area of England to facilitate group meetings.
