If the images are always linked and not actually embedded/included on the page itself, you could do it like this:
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Determine what post type this needs to happen on. Consider creating a specific post type where the figures always renumber, so that you aren’t renumbering on other parts of the site where it might not be desired. Or, consider creating a different Page Template so that you’ll only renumber when that particular template is used.
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Have the author always link to the figures with the same text – i.e. always have the link text be “see figure” or “See figure”. Go back and edit existing links so they are always consistent, and make sure that the words “see figure” are only used within the links you want to number.
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Create a JavaScript, which you enqueue only on whatever post type or template you need it on. Using jQuery you can find all links with link text “see figure” and increment a counter so you’ll replace the link text as “see figure 1.1”, “see figure 1.2”, and so on.
The JS is a bit out of scope on this site, but basically you need to select all links (“a” elements) that contain the text “see figure” (or your chosen text), then create a variable to hold your number, then do a foreach loop to replace the link text with “see figure 1.x” and increment x.