Here are some synonyms for discreetly:
* Privately
* Secretly
* Quietly
* Subtly
* Unnoticeably
* Confidentially
Here are some examples of how "discreetly" might be used:
* "He discreetly slipped a note into her hand."
* "The police discreetly observed the suspect's movements."
* "She discreetly asked for a private room to discuss the matter."
In contrast to "discreetly," the word "discrete" refers to something separate and distinct. For example, "There are three discrete units in the building."