"extend the frontier" is correct and usable in written English.
It is often used when referring to the expansion of boundaries, in terms of geography, science, technology, and so on. For example: "The exploration of outer space extended the frontier of scientific knowledge."
Later, it was exhilarating to watch Parametric Technology repeat the pioneering process and extend the frontier once again.
Is it the Puritan heritage, the constant battle to extend the frontier, the geographical and ethnic diversity, the aspiration for newness and greatness, the belief in America which underlies even denunciations of capitalist America, as in Arthur Miller's Death of a Salesman (include that, by the way,) or the creative life it puts into "low" genres?
It is an attempt to extend the frontier of the organism for biotechnological applications.
The purpose of the handbook is to (1) describe and elucidate the state of the field and (2), where appropriate, extend the frontier of DEA research.
Despite these internal difficulties, Otto found time to strengthen and to extend the frontiers of the kingdom.
Our nation's founding commitment is still our deepest commitment: In our world, and here at home, we will extend the frontiers of freedom.
Both sides believe that they are heirs to the civil-rights movement and are trying to extend the frontiers of human freedom.
They built up a navy to trade as well as to challenge the Byzantines and underscore the ʿAbbāsid caliph's failure to defend and extend the frontiers.
Invented on American soil and widely viewed as a symbol of national greatness, the airplane promised to extend the frontiers of the United States "to infinity," as Pan American World Airways president Juan Trippe said.
Two: Which works have seemed to you to extend the frontiers of your own mind so that you'd like them sooner or later to be much better known?
