be sulking
The German word 'nachtragen' is used to express the act of sulking or harboring resentment. It can be used in a similar context as the English phrase 'to hold a grudge'. For example, 'Er trug ihr lange nach, dass sie ihm nicht geholfen hatte.' translates to 'He sulked for a long time that she hadn't helped him.'
I have to make an addition to my diary.
The German phrase 'etwas nachtragen' usually implies adding something retrospectively, in this case, an entry to a diary.
She is still holding his mistake against him.
The German phrase 'jemandem etwas nachtragen' is used to describe the act of not being able to let go of something, often a mistake or misdoing by somebody else.
Could you please add the additional costs?
In this context, 'nachtragen' takes the meaning of adding something to an existing list or calculation, here, the additional costs to the original amount.