Synthetic DNA aptamer receptors could boost the prospects of carbon nanotube (CNT)-based electronic biosensors if signal transduction can be understood and engineered. Here, we report CNT aptasensors for potassium ions that clearly demonstrate aptamer-induced electrostatic gating of electronic conduction. The CNT network devices were fabricated on flexible substrates via a facile solution processing route and non-covalently functionalised with potassium binding aptamers. Monotonic increases in CNT conduction were observed in response to increasing potassium ion concentration, with a level of detection as low as 10 picomolar. The signal was shown to arise from a specific aptamer-target interaction that stabilises a G-quadruplex structure, bringing high negative charge density near the CNT channel. Electrostatic gating is established via the specificity and the sign of the current response, and by observing its suppression when higher ionic strength decreases the Debye length at the CNT-water interface. Sensitivity towards potassium and selectivity against other ions is demonstrated in both resistive mode and real time transistor mode measurements. The effective device architecture presented, along with the identification of clear response signatures, should inform the development of new electronic biosensors using the growing library of aptamer receptors.