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.
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.