User interests manifest a dynamic pattern within the course of a day, e.g., a user usually favors soft music at 8 a.m. but may turn to ambient music at 10 p.m. To model dynamic interests in a day, hour embedding is widely used in traditional daily-trained industrial recommendation systems. However, its discreteness can cause periodical online patterns and instability in recent streaming recommendation systems. Recently, Interest Clock has achieved remarkable performance in streaming recommendation systems. Nevertheless, it models users' dynamic interests in a coarse-grained manner, merely encoding users' discrete interests of 24 hours from short-term behaviors. In this paper, we propose a fine-grained method for perceiving time information for streaming recommendation systems, named Long-term Interest Clock (LIC). The key idea of LIC is adaptively calculating current user interests by taking into consideration the relevance of long-term behaviors around current time (e.g., 8 a.m.) given a candidate item. LIC consists of two modules: (1) Clock-GSU retrieves a sub-sequence by searching through long-term behaviors, using query information from a candidate item and current time, (2) Clock-ESU employs a time-gap-aware attention mechanism to aggregate sub-sequence with the candidate item. With Clock-GSU and Clock-ESU, LIC is capable of capturing users' dynamic fine-grained interests from long-term behaviors. We conduct online A/B tests, obtaining +0.122% improvements on user active days. Besides, the extended offline experiments show improvements as well. Long-term Interest Clock has been integrated into Douyin Music App's recommendation system.