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To equip robots with dexterous skills, an effective approach is to first transfer the desired skill via Learning from Demonstration (LfD), then let the robot improve it by self-exploration via Reinforcement Learning (RL). In this paper, we propose a novel LfD+RL framework, namely Adaptive Conditional Neural Movement Primitives (ACNMP), that allows efficient policy improvement in novel environments and effective skill transfer between different agents. This is achieved through exploiting the latent representation learned by the underlying Conditional Neural Process (CNP) model, and simultaneous training of the model with supervised learning (SL) for acquiring the demonstrated trajectories and via RL for new trajectory discovery. Through simulation experiments, we show that (i) ACNMP enables the system to extrapolate to situations where pure LfD fails; (ii) Simultaneous training of the system through SL and RL preserves the shape of demonstrations while adapting to novel situations due to the shared representations used by both learners; (iii) ACNMP enables order-of-magnitude sample-efficient RL in extrapolation of reaching tasks compared to the existing approaches; (iv) ACNMPs can be used to implement skill transfer between robots having different morphology, with competitive learning speeds and importantly with less number of assumptions compared to the state-of-the-art approaches. Finally, we show the real-world suitability of ACNMPs through real robot experiments that involve obstacle avoidance, pick and place and pouring actions.