I've just started as postdoctoral researcher at a great institute. I imagine that they expect me to achieve good results and teach some classes.
But honestly, I feel that I still need to learn a lot more on many topics. So, is it a good idea to dedicate a few hours of my day to learn new topics? Or should I focus only on what I already know and on how to apply it in order to obtain more results?
It is a new stage of my life and any tip that may improve me as a researcher is very welcomed.
While "learning new subjects" vs "focus on applying what I know" may sound like a dichotomy at first it really need not to be one: Try to apply the things you know to new problems and learn what you need to learn to do this successfully.
Put differently: Learn new things more focused on the problems you are facing. It is really rare that you encounter a problem that you can solve by just applying what you know. In most cases, the actual problem at hand has some new structure that can be exploited in some way and this usually forces you to read up something new.
On the other hand, it can not hurt if you learn some things that are not totally related to your current research just to broaden you expertise. I do this when I got stuck on my problems and, coincidentally, it happens frequently that I stumble upon just the right thing to help me with my current problem.
There is absolutely nothing wrong to dedicate a good fragment of your time to learn new things. Science is a dynamical thing and at some point you will be forced to learn new things/techniques etc (depending your field). PhD makes you master a rather small and specific area but to be a truly good researcher you should be able to see the bigger picture.
If you dedicate your time exclusively on the topics you already know then this could be seen as an incremental thing: applying what we know on new things is alright but it doesn't advance science: This needs to design new techniques probably using new tools from unexpected areas.
So, dedicate as much as you can on studying and expanding your knowledge/topics!
You could do both - learn new topics that interest you as well as applying what you already know to new innovations and discoveries. You may find that the new topics relate to your central discipline - allowing broader applications (I have found this with my own research).
There is nothing wrong with expanding your knowledge - just be mindful of the expectations of outcomes etc from your institution.
Another thing I found very useful is to spend some time developing new skills related to the academic interests (computer languages etc).
For most people, the postdoc will give the most bang for the buck if your primary focus is on strengthening your publications list.
To do this, additional study may be needed.
If not, and you can spare the time, you could set yourself a cap on what would be a reasonable amount or proportion of time to spend on learning things that are, at the moment, tangential.
