The ark of the covenant was the special box created in the Exodus story (see Exodus 25:17 - 22 and 30:6), and possibly looked like this:
So make no mistake, it was an important box!
But now see what Paul is saying: Jesus is that atonement cover. Paul qualifies his statement with 'through the shedding of his blood', so more precisely Paul is saying:
Yes Jesus-on-the-cross replaces the box. The actual physical box was somehow lost in history anyway, but Jesus being raised to life is very much alive today and so continues to be that ultimate place where people can meet with God and be made right once again.