Okay, so ...
baron writes a letter homedispatch to commander of the Iron Order units (swords, pikes, knights) in Caercas to join him quickly (force march)
...
bombardment and siege of the castle continues, aditionally, when the new units from Brosien arrive, baron will order them to show themselves marching around the castle (I assume the castle commander and his men do have partial insight into number and units position around the castle and banners they belong to, so they'll notice the reinforcements)
after parade, the new units will join the blocking force
...
meanwhile, baron writes a new letter to the castle's commander :
Sir,
you have my respect and respect of my men for the courage, trying to stop the force standing against you. You have delayed my progress furher into Taeghas and thus fullfilled your role and duty to your Lord. Now, your courage and bravery will soon turn from respectable to meaningless. Your further defense will mean nothing in this war, only will result into inevitable death of you and your men. Before the walls of your castle fall, I offer you another chance for honorable surrender.
Aruvor Raemel,
Black baron of Roesone
Knight of Stormlord