I am a postdoc working on a research project, which is funded by a grant that runs for 3 years.
After my first year working on the project, I identified a problem which could potentially lead to a new research direction, but it is not directly related to my current project. I am required to work on the problems defined in my current project proposal.
What should I do in this case, given that I may need to wait for another 2 years before I can possibly work on the new problem?
Now you are a postdoc and not a graduate student anymore. As such, you will have many research ideas, that you will not have the time to implement yourself. So, it is time for you to start delegating this work to "less experienced" workforce than you. That means undergraduate, master or PHD students. So, you should discuss it with your advisor that you have a new idea and that you are planning to propose a new undergraduate or MSc thesis. Perhaps he might even propose, working with a graduate student who is a bit stuck at his current stage of his / her PHD, so working in your new idea might be beneficial to both of you.
In any of these cases, co-authorship issues should be discussed early and thorough. For undergraduate, MSc students usually the assumption is that they do most of the work (it is their thesis after all) but you write the paper and you get to be first author. For teaming with PHD students, things are a little bit trickier, so these issues should be discussed in detail, BEFORE the cooperation begins. Also, make sure that your PI is OK not to be included in the subsequent publication (since this is your idea after all). Of course, if you want to include your PI in your "additional" publication then by all means, go ahead (this will also help you bend his objections about the time you will spend on your new project). But if you do not, make sure you discuss it before doing it, so you will not get into hot water.
In this scheme, not only you can multiply the number of your publications more easily and faster but also you help other people, who might be your future collaborators. So, you really have nothing to lose.
Your research project doesn't own you ... it merely pays the bills. If you got an interesting idea related to your project, you have an ethical obligation to discuss this with your advisor. If your idea has nothing to do with your project, you have every right to spend your free time developing it, as long as you maintain appropriate time and effort on your project.
You might consider starting a journal to record your ideas. I'm guessing that your new idea is pretty good, but you will certainly have many, many more good ideas over your career. This might be a situation when it is best to spend your time thinking, refining, and planning -- as opposed to acting. Having ideas is certainly very good, but you can't pursue all of them. Since you are just starting out your career, I would focus on being as productive as possible with your current project and enhance your skills. You will find that one idea leads to another, and you will eventually have way more ideas than time and money. This is certainly much more desirable than newly minted PhD's who are struggling to come up with a project. Good luck!
