Try This one:
var TheMember = from member in TSDataBase.Staff
where member.StaffID == EmpID
select new
{
Name = member.Name,
Position = member.Position,
TimeSheetData = from sheet in TSDataBase.TimeSheet
where sheet.StaffID = member.StaffID
and sheet.tsDate<datetime.today
select sheet;
};
The first part selects the staff data. As I don't know about the members of there two classes, I made my assumptions. The second part (like a inner select) will fill the TimeSheetData member of the newly created anonymous class (you should create a dedicated class for that) will be filled with the timesheet "records" related to that staff member according to the condition.
Update:
By the way your question and your fluent api query are confusing. You tell about tables, but you select from an embedded IQueryable. Let's asume used EF DatabaseFirst, and you have navigation on place. Than the above query will look like this:
var TheMember = from member in TSDataBase.Staff
where member.StaffID == EmpID
select new Staff
{
Name = member.Name,
Position = member.Position,
TimeSheet = from sheet in member.TimeSheet
where heet.tsDate<datetime.today
select sheet;
};