The phrase "illicit affair" refers to a secret and forbidden romantic relationship between two people, usually because one or both of them are already in a committed relationship with someone else. Full definition
I don't write chronologically from A to B — to do so would be to leave one open to the dreaded writer's block / inertia / laziness that comes from the tedium of «one damn thing after another» — so I tend to mix around, darting from, say, Owen Tudor's illicit affair with Katherine of Valois to the moment when Richard III has his skull brained in on the fields of the battle of Bosworth. (totalpolitics.com)
I was sorry that the author chose to include this perceived illicit affair between teacher and student for the simple reason that there seems so much of it in the real world today; I hoped the novel would avoid the commonplace altogether. (bookbrowse.com)