Footnotes

For incrementing footnote numbers across files in a book file you can use this script:

https://creativepro.com/files/kahrel/indesign/book-footnotes-continue-numbering.html

I’m also unclear if you have a single .indd file divided into sections that you are referring to as chapters, or if you have created a book file (.indb file) that collects multiple .indd files and manages them in a list. 

Peter addressed the first scenario so I’ll address the second. InDesign can’t increment footnote numbers across chapters in a book file, but you can open each individual chapter and manually set the starting number.

Is this one document, or several collected as an InDesign Book?

For a single file, simply click the outport of the last text frame from chapter three and click the loaded cursor into the first text frame of chapter 4.