"extend its role" is a correct and usable phrase in written English.
You can use it when you want to describe when an entity (person, thing, organization, etc.) has the opportunity to expand upon its existing responsibilities. For example, "The school district decided to extend its role in promoting physical education by providing additional supplemental resources to teachers."
The reluctance of the government to acknowledge that the funding of core costs and longer term strategic funding will be necessary if it wants the charity sector to extend its role in the delivery of public services is a fundemental problem.
Now the BBC wants to extend its role into IDTV and to become one of the main gateways to the Internet.
The Guardian can also disclose that the Scottish Police college could soon extend its role in the Maldives by helping run degree courses for a new policing academy, despite the growing international condemnation of Maldives police conduct over the last 10 months.
As such, soil science needs to vigorously become more interactive and extend its role beyond traditional agriculture.
Although the Staff College had previous experience in this field, the PPDP feasibility study provided opportunities to extend its role in primary care development.
This relatively long half-life for an effector protein allows SopB to extend its role from the early stages of invasion through to the intracellular phase of Salmonella survival.
Moreover, the involvement of SIRT7 in attenuation of ER stress and prevention of fatty liver disease formation (Shin et al., 2013), further extend its roles in maintenance of metabolic regulation.
As local government is told to rein in its reach, the private sector is extending its role in delivering services.
The organization later extended its role to the protection of a number of UN-declared "safe areas".
The next year Motorola extended its role in the U.S. consumer market by introducing the first television set for under $200, the Golden View.
In preparation for the lunar landing, NASA undertook the two-person Gemini spacecraft and recovery project with McDonnell Aircraft, which had been the prime contractor for Mercury, thus extending its role in the space program.
