Okay, where you put the  up in the biography is where you need to put the <ref>citation</ref>. Nothing is showing now, because you have the <ref> tags after the <references/> tag, which is what generates the footnotes, but it only generates footnotes from <ref> tags that appear above it.
As to what to put into the citation, unfortunately, the source you're using doesn't seem to generate URLs that point to the search result you're looking at. So, in that case, I'd put something like this:
<ref>New Zealand Government: Birth, Death and Marriage Historical Records: Registration Number: 1887/17112, Family Name: Hook, Given Name(s): Ada Pearl, Mother's Given Name(s): Martha, Father's Given Name(s): Freind, Still Birth: -. https://www.bdmhistoricalrecords.dia.govt.nz
It's not as good as if you could point directly to the record, but it's probably as good as you can do with that web site.