"Covering up" means hiding something from view or concealing the truth, often to avoid blame or shame. It can also mean putting on clothes or layers to protect skin from sun, cold, or attention.
Being a salesman and an actor were not that dissimilar: It is a good lesson in covering up your feelings. No one wants to buy from someone who looks depressed. Dougray Scott
Born down in a dead man's town, The first kick I took was when I hit the ground. You end up like a dog that's been beat too much, Till you spend half your life just covering up. Bruce Springsteen
Managers who are skilled communicators may also be good at covering up real problems. Chris Argyris
Yes, all right, Landsman understands, so go shit in the ocean, that he made not the right but the only choice. He understands that the necessity of covering up for the dark deeds of the boys in the top drawer is one that nozzes have been making into a virtue since the dawn of police work. Michael Chabon
If the government is covering up knowledge of aliens, they are doing a better job of it than they do at anything else. Stephen Hawking
I used to always buy clothes too big, but I should have showed off instead of covering up. Carey Lowell