The displacement of conventional synchronous generation by Inverter-Based Resources (IBRs) poses critical challenges to the frequency stability of Renewable Energy (RE) integrated power systems. An increased shift towards green energy by integrating RE sources that provide little or no inertia results in a high Rate of Change of Frequency (RoCoF) and deteriorated frequency nadir/zenith following a credible system disturbance. Prediction of frequency metrics, such as frequency nadir and RoCoF, immediately after disturbances will help grid operators to take preventive/corrective actions, such as the deployment of faster frequency control, to ensure secure and stable grid operation. This paper presents an easy-to-implement analytical method to estimate disturbance size in a power system immediately following a contingency which is then used for predicting frequency nadir. The proposed estimation method uses active power measurements from a limited number of monitoring nodes and an adaptive bus admittance matrix of the system for the disturbance size estimation. The estimated disturbance size is then used to predict frequency nadir using a Neural Network (NN) based method. The performance and accuracy of the presented approach are evaluated using a standard IEEE 39 bus system and a real-life Gujarat power system in India through extensive simulations in DIgSILENT PowerFactory, considering various cases of disturbance size, type, and location.