Current Emotion Recognition in Conversation (ERC) research follows a closed-domain assumption. However, there is no clear consensus on emotion classification in psychology, which presents a challenge for models when it comes to recognizing previously unseen emotions in real-world applications. To bridge this gap, we introduce the Unseen Emotion Recognition in Conversation (UERC) task for the first time and propose **ProEmoTrans**, a solid prototype-based emotion transfer framework. This prototype-based approach shows promise but still faces key challenges: First, implicit expressions complicate emotion definition, which we address by proposing an LLM-enhanced description approach. Second, utterance encoding in long conversations is difficult, which we tackle with a proposed parameter-free mechanism for efficient encoding and overfitting prevention. Finally, the Markovian flow nature of emotions is hard to transfer, which we address with an improved Attention Viterbi Decoding (AVD) method to transfer seen emotion transitions to unseen emotions. Extensive experiments on three datasets show that our method serves as a strong baseline for preliminary exploration in this new area.