Hmmm... doesn't sound like a phrase that is used commonly in the United States but the context suggests that there won't be any personnel covering (or staffing) the contracts department after 5:30. "Late cover" sounds like it describes people who stay late past normal business operating hours and "cover" any late requests.

"Late cover" or "late coverage" is business terminology referring to shifts in scheduling employees. So, they are letting you know that the department is closing early that day. So, if you need anything processed or normally call and speak to someone outside ordinary US business hours in their home location it will have to wait for the following business day.