What this means is that someone is trying to get rid of a large chunk without having a major impact on the market. This involves market feeling (=the ability to gauge just how much you can feed into the market without showing your real size) and/or the ability to place blocks of shares with investors.

You may recall the brouhaha surrounding Deutsche Bank's sale of quite a large block of Deutsche Telekom shares last year. In fact, the sale was handled quite nicely - the price didn't collapse until they had pulled it off (shame for those who bought the shares...).

If the term is on its own, you might use something along the lines of "selling without excessive slippage".

There is an expression in "broker's lingo" where the process of feeding an order smoothly into the market is referred to as "finessing an order", but I doubt whether someone outside this industry would really catch the drift...

PS If this is part of a sentence, let's see it!