The typical definition of static page is plain text file, typed by hand or generated by software either. By definition static pages cannot have back-end powered dynamic functionality.
There are quite a few approaches to integrating WP (or anything really) with static page, typical being:
- convert static page to dynamic
- completely – turn it into a page of WP site
- or partially – load WP core in it explicitly and retrieve/output data
- generate and overwrite static page from WP whenever corresponding data is edited
- add JavaScript to static page that retrieves data from WP and injects it into page