Flight delay prediction has become a key focus in air traffic management (ATM), as delays reflect inefficiencies in the system. This paper proposes LLM4Delay, a large language model (LLM)-based framework for predicting flight delays from the perspective of air traffic controllers monitoring aircraft after they enter the terminal maneuvering area (TMA). LLM4Delay is designed to integrate textual aeronautical information, including flight data, weather reports, and aerodrome notices, together with multiple trajectories that model airspace conditions, forming a comprehensive delay-relevant context. By jointly leveraging comprehensive textual and trajectory contexts via instance-level projection, an effective cross-modality adaptation strategy that maps multiple instance-level trajectory representations into the language modality, the framework improves delay prediction accuracy. LLM4Delay demonstrates superior performance compared to existing ATM frameworks and prior time-series-to-language adaptation methods. This highlights the complementary roles of textual and trajectory data while leveraging knowledge from both the pretrained trajectory encoder and the pretrained LLM. The proposed framework enables continuous updates to predictions as new information becomes available, indicating potential operational relevance.