Here is more context for the quotation in the question, taken from notatene.com's “History – Norway becomes independent – Year 1814” page:
– There was an emergence of state-bearing elite groups (civil servants and bourgeoisie) – we get an upper class. Norwegian society, was more diverse and characterized by greater differences between rich and poor. They spoke Norwegian case and was in front of Norwegian independence.
The lack of sense in that last sentence suggests it was not written by a well-educated speaker of English.
The phrase “state-bearing” may be jargon from some narrow field of study, or may instead be a word-for-word translation of a phrase idiomatic in another language but not in English.
All that aside, it appears that the sense FumbleFingers suggested seems plausible: “people who uphold or to some extent control the way the State operates”.
In the example below (from a 2007 Texas A&M University dissertation), that suggested sense is possible, although this context suggests state-bearing refers to a more exclusive class, a social or political elite like a nomenklatura:
During the 1960s, dissatisfaction with the dominant development aid strategies and their effect became palpable. Not only where there no signs of automatic trickling down of benefits of modern technology, but also large segments of the population missed out on the economic growth that followed in the wake of decolonization; the foreign aid benefited only the state-bearing elite. [Ravi Mallipeddi, Dissertation, 2007
Most of the seven results of a Google search for "state-bearing elite" refer to discussions of former or future Soviet-bloc regimes. Two examples follow.
As Rothschild observed, this caused “a rift between the Pilsudskist ‘state-bearing elite’ and the rest of society.” ‒ Ilya Prizel, 1998
In the above, Prizel quotes from a Joseph Rothschild article about Marshal Pilsudski of Poland. State-bearing elite may have been a term used by or of Marshal Pilsudski ca. 1920-1935.
In this way, the formation of state-bearing elite (comprising the old nomenklatura and the new biznesmeny) succeeded, and this elite subsequently began to centralize the revenues from the few profitable branches of the economy (oil, fisheries, alcohol, and subsidies from Moscow). Thus, potential challengers were blocked from accessing the resources ... ‒ Christoph Zürcher, 2007
This quote from Zürcher's ebook, The Post-Soviet Wars: Rebellion, Ethnic Conflict, and Nationhood in the Caucasus, equates state-bearing elite with nomenklatura (privileged members of Soviet bureaucracy) and biznesmeny (biznesmen is Polish for businessman with overtones).