The complexity of large language model (LLM) serving workloads has substantially increased due to the integration with external tool invocations, such as ChatGPT plugins. In this paper, we identify a new opportunity for efficient LLM serving for requests that trigger tools: tool partial execution alongside LLM decoding. To this end, we design Conveyor, an efficient LLM serving system optimized for handling requests involving external tools. We introduce a novel interface for tool developers to expose partial execution opportunities to the LLM serving system and a request scheduler that facilitates partial tool execution. Our results demonstrate that tool partial execution can improve request completion latency by up to 38.8%.