Glossary search should be applied automatically to the selected phrase.
Some design is needed for this feature. Some initial notes:
use dashed underline or similar on matched terms in the source document to indicate that there is a glossary match
click or hover terms to see the description and the current language translation (as available)
allow a panel to be opened that shows all the glossary terms and definitions
I think there are designs that include this panel, check those for where it should go.