Hey @trainoasis,
I think your best bet is to do a wp_ajax call. https://codex.wordpress.org/AJAX_in_Plugins
The action you hook onto that call should prepare any data your partial needs and then call Template() passing in the partial path and the data. See the thread I linked to above and @MWDelaney’s post about passing data.
The action could be a static method on a controller (the app controller, for example).
Does that help get you any further in the process?