Some (actually most) ATC units are very helpful and will try and (legitimately) get you a few minutes of slack. They will normally also allow the last few seconds of the Slot to be used, like LBA did for us yesterday. But you have to do your bit. And that means “Ready” when you actually are, rolling when you are cleared etc. But they do have limits. Typically you will be kept informed and together you can work out something that doesn’t waste loads of fuel or you taxiing around in circles. But and there are places and times when you hear “You have missed your Slot. You will return to the gate” or something similar. MUC will do that with pleasure, you can almost hear the glee in their voices. You are No. 6 to taxi, you WILL be No. 6 to depart, there will be eight arrivals ahead of you, you have allowed 20-25 minutes taxi... Not their problem!
PM