I’m still confused. Ingrid Bergman played Rick’s former lover.
Yvonne (played by Madeleine Lebeau) was in Rick’s before Ilsa (Ingrid Bergman) showed up. She approaches Rick and they have the following conversation:
Yvonne: Where were you last night?
Rick: That was so long ago I don’t remember.
Yvonne: Will I see you tonight?
Rick: I don’t plan that far ahead.
She turns and orders a drink from Sasha, but Rick tells her she’s had enough to drink and has Sasha take her home.
Renault sees the exchange and comments that Rick is careless in tossing away women and they he (Renault) may go pay her a visit.
Through that scene, we can infer that Rick and Yvonne had recently been lovers and that Rick, for whatever reason, had broken it off.