In the prefrontal cortex (PFC), higher-order cognitive functions and adaptive flexible behaviors rely on continuous dynamical sequences of spiking activity that constitute neural trajectories in the state space of activity. Neural trajectories subserve diverse representations, from explicit mappings in physical spaces to generalized mappings in the task space, and up to complex abstract transformations such as working memory, decision-making and behavioral planning. Computational models have separately assessed learning and replay of neural trajectories, often using unrealistic learning rules or decoupling simulations for learning from replay. Hence, the question remains open of how neural trajectories are learned, memorized and replayed online, with permanently acting biological plasticity rules. The asynchronous irregular regime characterizing cortical dynamics in awake conditions exerts a major source of disorder that may jeopardize plasticity and replay of locally ordered activity. Here, we show that a recurrent model of local PFC circuitry endowed with realistic synaptic spike timing-dependent plasticity and scaling processes can learn, memorize and replay large-size neural trajectories online under asynchronous irregular dynamics, at regular or fast (sped-up) timescale. Presented trajectories are quickly learned (within seconds) as synaptic engrams in the network, and the model is able to chunk overlapping trajectories presented separately. These trajectory engrams last long-term (dozen hours) and trajectory replays can be triggered over an hour. In turn, we show the conditions under which trajectory engrams and replays preserve asynchronous irregular dynamics in the network. Functionally, spiking activity during trajectory replays at regular timescale accounts for both dynamical coding with temporal tuning in individual neurons, persistent activity at the population level, and large levels of variability consistent with observed cognitive-related PFC dynamics. Together, these results offer a consistent theoretical framework accounting for how neural trajectories can be learned, memorized and replayed in PFC networks circuits to subserve flexible dynamic representations and adaptive behaviors.