Pursuing a research career in a university without teaching duties, is it possible?

Yes. In the UK such positions are called Research Assistants or Research Associates. There are also Postdoctoral Researchers.

These are full-time salaried researchers who are employed on specific grant funded projects. The only down-side is that they are often fixed-term contracts linked to the fixed term research grant; however, UK employment law does offer some protection, because if you land several sequential fixed term positions at the same institution you are regarded as a permanent employee with greater rights when the funding ceases.

Such positions are advertised in the Academic press (such as the Times Higher Education Supplement) or on jobs.ac.uk.

Some universities in the US have Research Professor positions available. These usually are non-tenured positions, and they often don't have any salary lines associated with them; the research professor's salary comes entirely from the research grants that the research professor brings in as a Principal (or Co-Principal) Investigator, or participates in as a Senior Investigator (someone else, possibly even from another university, is the Principal Investigator) on the research grant or contract. There are similar positions at the associate and assistant professor levels. Such positions are often created at the behest of the applicant: a hot-shot researcher with no interest whatsoever (and possibly no experience too) in teaching wants to bring his lab/research program from, say, industry or a free-standing research institute, to a university and offers to do so if the university creates a position from him.

In France the CNRS offers each year a few research-positions in a considerable range of disciplines. (The initial hiring is usually done at a level comparable to assistant professor.)

The recipient of such a positions is then typically assigned to some university where they will work in the laboratory corresponding to their field.

These are permanent positions, and there is an option for later promotions.

For certain disciplines there are other organization that offer similar types of jobs (such as Inria, for computer science).

With such a position it is also possible to supervise students, and it is often also possible to teach a bit on the side (if at some point, one wants to).

Thus, I would say, yes, this is possible. But, as said in another answer, there is a lot of competition.