using 4 explanatory continuous variables for the new data, one
explanatory continuous variable for the old data
So for the new model you used something like y ~ x1 + x2 + x3 + x4, but in the old model it was just y ~ x1?
If this is correct then it's not a surprise that you registered a higher AUC.
Also is x1 in the new model the same as x1 in the old model? I mean the same variable. Because if that's the case you could say that x1 impacts heavily on performance, but x2-x4 improve accuracy too.
You should compare the performance that you have between the old and new model (plus the old+new model), using the same explanatory variables (same number, same variables).
Also the number of observations should be the same for a meaningful comparison between the models.
If observations are randomly picked than you should also repeat k times for consistency, ie: repeat the 3 models on n observation sampled from your population.
what can I inference by the AUC of the old+new independent data, given
the AUCs previously mention
To me not much, because as I mentioned above the models are different. Try use the same number of variables first.