1640s, originally in English as a cookery term for a thickening agent for sauces, from French liaison "a union, a binding together" (13c.), from Late Latin ligationem (nominative ligatio) "a binding," from past participle stem of Latin ligare "to bind" (from PIE root *leig- "to tie, bind").
Sense of "intimate relations" (especially between lovers) is from 1806. Military sense of "cooperation between branches, allies, etc." is from 1816. The meaning "one who is concerned with liaison of units, etc." is short for liaison officer (1915).
<a href="https://www.etymonline.com/word/liaise">Etymology of liaise by etymonline</a>
Harper, D. (n.d.). Etymology of liaise. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/liaise