Is there a way InDesign can change italic to bold italic if the style definition has bold?

First things first. Create a character style for the italic bold text.

With that out of the way, do a find change looking for any manually styled italic with that Paragraph style and change it to that character style.

That little "+" sign you see means that the style is based on your original ChapterTitle style, but in this case something is changed from the original specification. In this case, it'd likely be the type styling applied in the Word document. You'd like it to be the type styling you want to apply in InDesign. But unfortunately, it's probably going to be best if you manually make the change you want to the text yourself.

Please let me explain.

I'd just about bet that the original text you want to apply your ChapterTitle paragraph style to is plain 'ol text in the Word manuscript. Except where the italics are applied in the Word file, in instances where your example Patient Safety example is indicated. No styles are applied in the Word document, only word styling, where the author selected the text and clicked the little I button turned the character from plain ol' text into plain ol'text with italics.

You placed the file leaving Word's type attributes intact because you wanted to maintain all the type styling the original author intended. That's a good thing, because you didn't want to strip all those attributes out of the manuscript and place it as roman/standard text, then have to manually highlight each relevant exception and resyle it manually yourself within InDesign. Or worse, miss instances of the author's type styling while trying to restyle it all yourself within InDesign.

But in this case, that bites you. Because the Word type is styled as italic, and when you click into the paragraph and apply your larger, bolded ChapterTitle paragraph style, it maintains the Word type styling as italic. And InDesign won't automatically change it to bold italic. The unfortunate exception that proves the rule. InDesign has tools which can globally change italic to bold italic for you, but that would then change the instances where the author — and you — wanted to use italic instead of bold italic.

If you haven't already laid out the entire book with lots of these examples, I'd just grumble and fix the chapter issues on the fly. If the book is already laid out, and you have loits of instances, you can use InDesign's advanced Find/Change features (Edit>Find/Change... menu command) to at least streamline the search and manually make the changes. But if you only have a few chapters where this occurs, automating the search may or may not be worth the extra effort. It's just something you gotta do to make things right.

Hope this helps,

Randy