Discrete here means using discretion, respecting issues of privacy and decency.

Having a word with someone means having a talk with them.

Having a discreet word with someone usually means you talk to someone in private - you take them apart at the coffee corner, or you move into a meeting room. It indicates the opposite of giving someone a public telling off. It is often considered unkind to criticize someone in public, in front of their friends or colleagues. Having a discrete word with them, you make sure they do get the message,but it is not a public event.

I feel compelled to correct my spelling after StoneyB's answer. The correct spelling is discreet, not discrete.

Discreet here means using discretion, respecting issues of privacy and decency.

Having a word with someone means having a talk with them.

Having a discreet word with someone usually means you talk to someone in private - you take them apart at the coffee corner, or you move into a meeting room. It indicates the opposite of giving someone a public telling off. It is often considered unkind to criticize someone in public, in front of their friends or colleagues. Having a discreet word with them, you make sure they do get the message,but it is not a public event.

I will have a discrete word them. Is not grammatical. You can have a word with them.

Discrete here means using discretion, respecting issues of privacy and decency.

Having a word with someone means having a talk with them.

Having a discreet word with someone usually means you talk to someone in private - you take them apart at the coffee corner, or you move into a meeting room. It indicates the opposite of giving someone a public telling off. It is often considered unkind to criticize someone in public, in front of their friends or colleagues. Having a discrete word with them, you make sure they do get the message,but it is not a public event.

Discrete here means using discretion, respecting issues of privacy and decency.

Having a word with someone means having a talk with them.

Having a discreet word with someone usually means you talk to someone in private - you take them apart at the coffee corner, or you move into a meeting room. It indicates the opposite of giving someone a public telling off. It is often considered unkind to criticize someone in public, in front of their friends or colleagues. Having a discrete word with them, you make sure they do get the message,but it is not a public event.