First, it is absolutely acceptable to have significant overlap (in terms of content) between the two literature reviews. Of course, you need to avoid plagiarism. The best solution is to rewrite the literature review from scratch. By doing this, you can also reassess if all content from the original review is needed in the new paper and whether the order in which you present information makes sense for the new paper (but see below).
To distinguish the new from the original literature review, there are several things to address:
- Most importantly, include a brief review of your first paper to highlight what was found there and use this to highlight why an additional paper is needed.
- Your continuation will address questions not covered by your first paper. Make sure to include sufficient background on these new questions in your new literature review.
- Add any relevant information that was published since your first paper.