Recently, an emerging application field through Twitter messages and algorithmic computation to detect real-time world events has become a new paradigm in the field of data science applications. During a high-impact event, people may want to know the latest information about the development of the event because they want to better understand the situation and possible trends of the event for making decisions. However, often in emergencies, the government or enterprises are usually unable to notify people in time for early warning and avoiding risks. A sensible solution is to integrate real-time event monitoring and intelligence gathering functions into their decision support system. Such a system can provide real-time event summaries, which are updated whenever important new events are detected. Therefore, in this work, we combine a developed Twitter-based real-time event detection algorithm with pre-trained language models for summarizing emergent events. We used an online text-stream clustering algorithm and self-adaptive method developed to gather the Twitter data for detection of emerging events. Subsequently we used the Xsum data set with a pre-trained language model, namely T5 model, to train the summarization model. The Rouge metrics were used to compare the summary performance of various models. Subsequently, we started to use the trained model to summarize the incoming Twitter data set for experimentation. In particular, in this work, we provide a real-world case study, namely the COVID-19 pandemic event, to verify the applicability of the proposed method. Finally, we conducted a survey on the example resulting summaries with human judges for quality assessment of generated summaries. From the case study and experimental results, we have demonstrated that our summarization method provides users with a feasible method to quickly understand the updates in the specific event intelligence based on the real-time summary of the event story.