If you leave Belgium permanently, prepare the declaration of departure to the municipality. For a temporary absence with return, consult the corresponding procedure before traveling.
If you have completed your studies in Belgium and wish to look for a job or create a business, a residence permit of up to twelve months can be requested under conditions. It is not automatic. The request must be submitted no later than fifteen days before your A card expires; check the supporting documents on the municipal form and with the Foreigners' Office.
To know more.
Extension of the residence permit on the UCLouvain website.