Accurate estimation of DL CSI is required to achieve high spectrum and energy efficiency in massive MIMO systems. Previous works have developed learning-based CSI feedback framework within FDD systems for efficient CSI encoding and recovery with demonstrated benefits. However, downlink pilots for CSI estimation by receiving terminals may occupy excessively large number of resource elements for massive number of antennas and compromise spectrum efficiency. To overcome this problem, we propose a new learning-based feedback architecture for efficient encoding of partial CSI feedback of interleaved non-overlapped antenna subarrays by exploiting CSI temporal correlation. For ease of encoding, we further design an IFFT approach to decouple partial CSI of antenna subarrays and to preserve partial CSI sparsity. Our results show superior performance in indoor/outdoor scenarios by the proposed model for CSI recovery at significantly reduced computation power and storage needs.