A

Step 1: Understanding electric field units.
The electric field (E) is defined as the force (F) per unit charge (q) experienced by a test charge placed in the field: $E = \frac{F}{q}$.
Therefore, the SI unit of electric field is Newton per Coulomb (N/C), which can also be expressed as Volts per meter (V/m).
Step 2: Analyzing the options:
Option A: $NC^{-1}$ - This is another way to express N/C, hence it is a unit of electric field.
Option B: $Vm^{-1}$ - This is Volts per meter, which is a unit of electric field.
Option C: $JC^{-1}$ - This is also equivalent to Volts, which is related to electric field but not directly a unit of electric field.
Option D: $JC^{-1}m^{-1}$ - This can be interpreted within the context of electric field, as it can be rearranged to show direct relations to electric field units.
Conclusion: The correct answer is Option A, as it is not conventionally referred to as a unit of electric field in a clear context.