In the documentation you see that approaching elements of NumericArray systematically is by using Part, therefore the only way of implementing 1+na is using a loop (that generates lists)
for example
na = NumericArray[Range[10], "UnsignedInteger8"]; NumericArray[
Table[Part[na, i] + 1, {i, 10}], "UnsignedInteger8"]
or
NumericArray[Table[na[[i]] + 1, {i, 10}], "UnsignedInteger8"]
quite disappointing I would say
Even functions such as Fold or SequenceFold do not work with NumericArray (not to say the so basic function Map as you mentioned).
Pattern Matching also cannot be used with NumericArray
I certainly hope it will be changed in the future