Hi all I'm new and looking for some help.

We have had our goldfish for 2 years now and on 2 separate occasions have tried adding another fish (we know the tank is big enough 15l) On both occasions the new fish has died within 1-2 days. I wondered if the original fish was killing the new ones. How should we introduce new fish to the tank?

Goldfish are definitely NOT territorial.
They actually like new fish to play with (and bump into accidentally).
it is a very slim chance that your old fish is killing the new ones, but perhaps it is through indirect means-your tank may have strange diseases in it from your old fish that do not bother it but kill anything new that is unused to such diseases.
when you find the new fish dead in the aquarium, what does it look like? (are there scales missing, red marks/bruises/wounds, is there damage to the fins, what do the gills look like)
Also, how are you introducing the new fish to the tank? your problem may be acclimation fallacies-this happens a lot, so if that is the case, don't feel bad.