It works the same way as if you're caught with animals without a license. You will have a list of things that need to be done and a timescale to complete them. The only change to this may be if there is a risk to either public health or the animals
Thats not correct. A licence cannot be granted retrospectively. Either you are licenced or not. So if you keep specimens you are not licenced for and get caught you cannot then ask for a licence. The local authority will seize them and dispose as they see fit.
I'm not sure on the 28 day grace period either. I'm not aware of that in any part of the DWAA. Off the top of my head there is mention somewhere of a 72 hour period which is basically to cover transport times. As the owner you must have he licence in place first.