Emotion recognition in conversation (ERC), the task of discerning human emotions for each utterance within a conversation, has garnered significant attention in human-computer interaction systems. Previous ERC studies focus on speaker-specific information that predominantly stems from relationships among utterances, which lacks sufficient information around conversations. Recent research in ERC has sought to exploit pre-trained large language models (LLMs) with speaker modelling to comprehend emotional states. Although these methods have achieved the encouraging results, the extracted speaker-specific information struggles to indicate emotional dynamics. In this paper, motivated by the fact that speaker characteristics play a crucial role and LLMs have rich world knowledge, we present LaERC-S, a novel framework that stimulates LLMs to explore speaker characteristics involving the mental state and behavior of interlocutors, for accurate emotion predictions. To endow LLMs with these knowledge information, we adopt the two-stage learning to make the models reason speaker characteristics and track the emotion of the speaker in complex conversation scenarios. Extensive experiments on three benchmark datasets demonstrate the superiority of LaERC-S, reaching the new state-of-the-art.