Hithgol is convinced the spear you found is indeed the mythical Aiglos.
'Legolas has scouted the location of the spear and informed me that it is indeed the lost spear of Aiglos. I understand that you might not share the same enthusiasm as I, but let it be known to you that this relic is of great pride to all Elves. During the Second Age, Gil-galad wielded Aiglos on the slopes of Mount Doom, lending to the defeat of Sauron. I know this, for I was there.
'Go, speak with my apprentice, Coldan. He should hear the news. Also I would like you and Legolas to retrieve the spear.'
Coldan can be found at the Udûn Foothold. Legolas can be found at the Ruins of Díngarth.
You should talk to Coldan and Legolas.
Hithgol can be found at the Ruins of Díngarth.
You should speak with Hithgol.