how to refresh table after an operation ?

Hi,
I have a datatable, the first column show agencies assigned to this row, in another column I have a button that when clicked show a form to assign new agencies to this row, everything work well, but for the new agencies added I have to refresh the page to see them, is there any way to add them as soon as I click the button "Assign" ?

here is an image showing what I am talking about :

http://s18.postimg.org/9xtvp7w6x/rr_Agency.png

Thanks.