What version of InDesign? What computer platform?
You'll have to acquire a Goudy Old Style font which includes those accents. What language are you trying to include?
If you have InDesign CC, look to Typekit for Goudy Old Style. You can check the languages it supports on Typekit.com.
There are a variety of websites which sell fonts, and they usually make it clear which languages are supported.
Thank you for your help. I am using Indesign CC 2015 on Windows 10 in English language. I have the font Goudy Old style. Don't quite understand how I will know which Goudy Old style includes the accents.
The Typekit Goudy Old Style doesn't have the Z accent you need. I just checked.
The "Goudy Old Style Std" font that Adobe used to sell has this character. I think the Eastern European languages include that glyph. If you use the Glyphs panel in InDesign and choose Extended Latin A in the Show menu, I think you can tell.
When I searched for "Adobe fonts sell" it seems they don't sell them from their website any more, but from other font vendors. "Find perpetual licenses for Adobe fonts from Fontspring and other resellers."
Go to the Fontspring website and look for that font. See what languages it supports.
Thanks Steve for all your help. It is much appreciated.