clear (one's) throat

1. Literally, to cough or make a guttural sound in an attempt to relieve a blockage in the throat, as is often caused by phlegm. I'm worried that I'm getting sick because I've had to clear my throat constantly all day long. Your allergies must be bad today if you have to clear your throat every two seconds. I turned away from the microphone and cleared my throat before I began making announcements.

2. To make a coughing sound in order to attract attention. When the boss cleared her throat, we immediately stopped talking so that she could start the meeting. Once I cleared my throat into the microphone, everyone quieted down and I could start making my announcements. I only started yelling because I'd cleared my throat multiple times and the students still wouldn't stop talking.

clear your ˈthroat

cough slightly, especially before speaking or to attract somebody’s attention: The lawyer stood up, cleared his throat and began to address the jury.