Large language models (LLMs) are increasingly deployed with task-specific adapters catering to multiple downstream applications. In such a scenario, the additional compute associated with these apparently insignificant number of adapter parameters (typically less than 1% of the base model) turns out to be disproportionately significant during inference time (up to 2.5x times that of the base model). In this paper, we propose a new zero-latency fused low-rank adapter (zFLoRA) that introduces zero or negligible latency overhead on top of the base model. Experimental results on LLMs of size 1B, 3B and 7B show that zFLoRA compares favorably against the popular supervised fine-tuning benchmarks including low-rank adapters (LoRA) as well as full fine-tuning (FFT). Experiments are conducted on 18 different tasks across three different categories namely commonsense reasoning, math reasoning and summary-dialogue. Latency measurements made on NPU (Samsung Galaxy S25+) as well as GPU (NVIDIA H100) platforms show that the proposed zFLoRA adapters introduce zero to negligible latency overhead.