Are monks allowed by Church law to set up a religious order for clergymen with a particular profession (ex. developers)? Imagine that there is a Catholic monk, who is also a full-stack developer, who, after much thinking wants to set up a religious order for clergymen who code. We have heard of clergymen (monks, priests) who are professors of various academic subjects, such as history and quantum physics. But I haven't heard of a particular religious order of clergymen who are collectively historians, scholars, etc. 

Is he qualified by Church law to set up a religious order? If yes, is he allowed to define in that religious order that the people signing up in there have to be/train to become developers? If yes, what are the requirements for setting up such religious order?

Thanks!
Monica, generally speaking, there is are typical pathways under which a person who wanted to set up a community of like minded individuals could do so and get some sort of ecclesiastical recognition for the community. The way it would be most likely to happen would be that the person recruits others to join his community, then seeks ecclesiastical recognition for that community. There is no reason that a "monk" could not do this, but it would be more likely to be someone who is not already a monk, as a monk is a man who is already part of an established community. The title "monk" is typically used for a person who is not ordained, and while he might be able to recruit to his proposed community people who already are, it is more likely than not that there would be unlikely to be "clergymen" among them, as clergymen are already ordained, and it is not common for ordained people to come under the authority of a lay person in ecclesiastical affairs. 

The exact process and procedure by which such a group would be set up would depend upon a number of factors. A small group operating in one place might be able to set up such a community with the permission and oversight of the local bishop. A national group with several communities in different places within the same country might need the permission and oversight of the appropriate National council of bishops; an international community, with communities widely distributed around the globe might need the permission and oversight of the appropriate office of the curia. The exact procedures to be followed might depend upon the size of the group. 

I suspect that someone who is highly motivated, and dedicated to setting up such a group as you propose could do so, by recruiting members, and working with the appropriate offices of the church. In fact, if I remember correctly, some years ago, I happened across the website of a monastery (operating under the Fransiscan rule, in Arizona, US, if I recall correctly) whose members supported themselves and the mission of the monastery by doing internet work. At the time their website was recruiting members with skills in several areas related to internet page design and creation. Regrettably, I no longer remember the exact name of the monastery, but one particular characteristic I remember of the monastic website was that the name of the title of the brother who was responsible for running the website was "webservant", rather than the then more common "webmaster".