Try:
string input = "08:00,11:00|11:00,13:00|13:00,16:00|";
List<TimeSlots> list = input.Split(new char[] {'|'}, StringSplitOptions.RemoveEmptyEntries)
.Select(ts => { string[] parts = ts.Split(',');
return new TimeSlots { StartSlot = parts[0],
EndSlot = parts[1] }; })
.ToList();