You have returned the last of the Silithair to Aragorn, and now the time has come for Narsil to be reforged.
'The time has come, ${PLAYER} -- Narsil will be reforged.
'Will you accompany me to the forges? The work will take some time, but I would have you there at Andúril's making. Speak with me when your affairs are in order, and we can walk there together.'
Aragorn is in one of the guest rooms of Elrond's House.
The Elf-smiths of Imladris will reforge the blade that was broken, and Aragorn is waiting to walk with you to the forges where it will be done.
Aragorn is in one of the guest rooms along the road that winds up the southern slope of the Vale of Imladris.
Andúril, Flame of the West, has been forged from the shards of Narsil, and Aragorn is waiting to speak with you.