My department has changed its favorite fields of research. What are the consequences?
I'm afraid I find the question rather vague.  You write


  When I was hired to a math department (in the US) my field was among the favorite directions in the department. 


I have spent my entire professional life in math departments in the US, and I was not aware that they (we?) have "favorite directions."  Even the smallest departments I know have at least four different research areas represented, and the general attitude / expectation is that everyone should be collegial and helpful with each other while feeling that their own area is the "favorite" and promoting accordingly.  

It is true that often different research groups have different sizes or different profiles.  In my department for instance the number theory group has been larger than the analysis group (and had more students, offered more courses, organized more conferences and so forth...) in the time I've been there.  But there is no explicit, systemic way in which number theory is promoted over analysis in my department: in fact we have hired in both groups in recent years.  


  Few years later the department decided to put more attention on some other areas of math. 


Again, what does that mean?  Do you mean in terms of hiring initiatives?  If so, maybe you have nothing to worry about: hiring initiatives are very often cyclic: departments target areas where the ranks have shrunk in recent years.  I have never in my life heard of a hiring initiative whose express purpose is to deemphasize or somehow lessen in any way the stature of faculty who are already there.  Why in the world would a department agree to that?  Even if a "lessening" of a current research area was in the best interest of the majority of the current members, faculty have more solidarity and longsighted worries than that: first they came for the analysts...


  E.g. whether my research will be considered to be less important for the department from some point of view? Will I get more administrative duties? Will it be harder to get grants for my research? Any other consequences?


Again, it seems really impossible for us to answer these questions.  The first one is excruciatingly vague. Everyone's research may be considered to be less important for the department from some point of view: if it's too theoretical then how is it contributing to the world really, and if it's overly applied then it's, you know, not as cool to pure mathematicians.  Will you get more administrative duties is certainly a question to ask the other members of your department.  I don't really understand why this would affect your ability to get external grants, but then I don't really understand what you're talking about.

In general this is something that as a tenured professor you absolutely need to discuss with your colleagues.  Honestly, you sound like you don't understand the whole thing very well.  I urge you to get a clue by talking to your colleagues, repeatedly and protractedly if necessary.  Being tenured means your colleagues need to listen and address all your questions and concerns.  It's time for you to use that power.