1.
If you cover something or someone up, you put something over them in order to protect or hide them.
He fell asleep in the front room so I covered him up with a duvet.
PHRASAL VERB: V n P, also V P n (not pron)
2.
If you ~ something that you do not want people to know about, you hide the truth about it.
He suspects there’s a conspiracy to ~ the crime...
They knew they had done something terribly wrong and lied to cover it up...
How do we know you’re not just covering up for your friend?
PHRASAL VERB: V P n (not pron), V n P, V P for n
see also cover-up