Incorporating large image-text foundation models such as CLIP has substantially improved the performance of the multimodal video retrieval task. However, how to practically sample the frames from a video and aggregate the frame features into a video representation is still an open research question. In particular, real-world deployment scenarios, such as embodiment within consumer electronics or cloud-based inference pipelines, require two key facets of retrieval (representation building and search) to be computationally light and fast. In this paper, we propose AdaCLIP, a computation- and latency-aware system for pragmatic multimodal video retrieval. AdaCLIP consists of a learning-based frame selection module to select informative frames and a query-independent frame aggregation module to obtain strong video representations from the frame features. Specifically, in the frame selection module, we introduce a differentiable Hard-Top-k algorithm to sample a subset of the frames while optimizing the performance of the video retrieval task in an end-to-end manner. Moreover, to be latency-aware, we also propose a query-independent lightweight approach, MLP-Score, to aggregate the frame features into the video representation, which offers up to 142x speedup on GPU and 822x speedup on CPU in similarity search time compared to query-dependent matching methods. Experimental results on several popular video retrieval datasets confirm the effectiveness of AdaCLIP.