How can I get rid of the metallic taste in my mouth after taking clarithromycin?

Patience! Tthe metallic taste dissipates once you have completed your course of clarithromycin. Hang in there, finish the entire prescription. If you cannot tolerate the taste, talk to your physician about a change to a different type of antibiotic.
Brush. Both your teeth and tongue (better yet, use a tongue scraper), rinse afterward with an anti microbial mouth rinse and drink lots of water. Symptoms will dissipate when therapy is complete.