After OTAs end in mid-June, most NFL front offices take some time off. The return date is generally after the 4th of July holiday.
Since we're now post-holiday, it's a good bet that the Chiefs front office is getting back to work this week to start (or continue) working on the rest of the draft picks that remain.
The last five you can pretty much count on being done before the Chiefs depart for training camp on July 29.
The first one, Berry, may be a different story. The Chiefs are (or will be) surely working with Berry's agent, Chad Speck, to get a deal done. It's a two-way street with these high draft picks so if nothing is done by 1:50 p.m. July 30, the first practice of training camp, both sides will be to blame.