If you tell someone to hurry up, you are telling them do something more quickly than they were doing. Franklin told Howe to hurry up and take his bath; otherwise, they'd miss their train Hurry up with that coffee, will you
If you hurry something up or hurry it along, you make it happen faster or sooner than it would otherwise have done. if you want to hurry up the application process Petter saw no reason to hurry the divorce along. = speed up