Is Derris-Kharlan's tree in Tales of Symphonia it's original one, or it's new one?
The Tree mentioned in Tales of Symphonia: Dawn of the New World by Tenebrae is the original one as Tales of Symphonia is set before the events of Tales of Phantasia


  Aselia (アセリア Aseria?) is the name of the world in which Tales of Phantasia takes place. ... as well as the combined world of Sylvarant and Tethe'alla from prequels Tales of Symphonia and Tales of Symphonia: Dawn of the New World.


Source: Aselia

according to the wiki linked, the Elves of Derris-Kharlan came to Aselia and transplanted the Kharlan Tree from Derris-Kharlan bringing life the the planet while, the elves took a cutting from the Kharlan Tree to replant it on Derris-Kharlan (as opposed to taking a cutting and planting it on Aselia)

it is this cutting that would have died between the gap of Tales of Symphonia: Dawn of the New World and Tales of Phantasia and thus the tree that Dhaos was looking to get a seed from is the new tree that was born after the events of Tales of Symphonia. 

this is backed up that in Tales of Phantasia Martel is Guarding the Tree





and Martel was only born as a Guardian Spirit of the tree after it was reborn in Tales of Symphonia