Is it better to submit a new research grant proposal or an extension of previous work?
There is no one-size-fits all answer. The key factors to consider are: (1) alignment to the funder's mission and (2) credibility.
Alignment to the funder's mission. Different funding agencies have different motivations. Some have a particular capability gap (whether mundane or extraordinary) and want to fund the group most likely to fix it. Some routinely fund well-established university groups and just want to see progress. Others specifically exist to fund high-risk, high-reward endeavors. Whether to propose &quot;incremental&quot; advances based on past research or &quot;revolutionary&quot; advances will depend on the funder's needs.
Credibility. Even for high-risk programs, successful proposals will usually provide a basis of confidence that the proposed idea will be successful (i.e., simply writing down some crazy idea to &quot;extend the boundaries of science&quot; will not be enough). In some cases, this basis of confidence could be the involvement of the proposal authors themselves (due to their publication record or performance on other programs). In other cases, this could be that a proof-of-concept of the proposed idea was already carried out and gave good results.