During the course of a research project, one may have new, more promising, ideas that were not foreseen and thus not covered in the original research proposal. What should one do in this case? Is it all right to work on the new idea under the original proposal? Or should one stick to the lines suggested in the original proposal and perhaps submit another proposal for the new idea although this means that one has to wait before he can work on the new idea?
There's two opposing forces here:
You're probably not doing research if you can say exactly what you are going to do beforehand in the research proposal. At the heart of research is exploration. Hence it is expected that you demonstrate some agency and adapt the research as you explore the topic more.
On the other hand, the people who fund you are funding you to work in the area of the proposal. Switching to a completely disconnected topic on a whim is (generally) not an option.
How far can research deviate from the original research proposal?
This is difficult to give a concrete answer to and it will differ from fund to fund. Most generally, if you can show the funding body a path from what you proposed to what you ended up doing (i.e., you can show that your intent was to follow the proposal, but you discovered new evidence that a better alternative was possible and you followed that alternative instead), then I think you're on safe ground.
In other cases, it will depend entirely on what your funding body is looking for and how they justify their funds to their bosses. You will have to try understand what the objectives of the funders are: is it publications, creation of a product, teaching and dissemination, contributing towards some high-level national/EU directive, etc.? Will your new direction likewise satisfy those objectives under what was originally agreed in the proposal? These are important questions. (Even if you stuck steadfastly to the topic proposed, groking the motives of your funders and what they will look for during reviews is vital for success. If you understand these motives well enough, then as a side result, you'll have the answer as to how much deviation is acceptable or even desirable.)