events on objects

Good evening, sorry for the inconvenience, I would like to take this opportunity to wish you all a peaceful Easter holiday.
I wanted to ask if in datatable there is the possibility of activating events in response to actions carried out on objects of the DataTable, that is, on two parent/child tables, I need to reset the child table when I click on the paginator buttons, or when I write in the search box, or when I click on the "X" of the search box, I attach an image that explains my question, thanks for any support.