Intent discovery is a crucial task in natural language processing, and it is increasingly relevant for various of industrial applications. Identifying novel, unseen intents from user inputs remains one of the biggest challenges in this field. Herein, we propose Zero-Shot-BERT-Adapters, a two-stage method for multilingual intent discovery relying on a Transformer architecture, fine-tuned with Adapters. We train the model for Natural Language Inference (NLI) and later perform unknown intent classification in a zero-shot setting for multiple languages. In our evaluation, we first analyze the quality of the model after adaptive fine-tuning on known classes. Secondly, we evaluate its performance in casting intent classification as an NLI task. Lastly, we test the zero-shot performance of the model on unseen classes, showing how Zero-Shot-BERT-Adapters can effectively perform intent discovery by generating semantically similar intents, if not equal, to the ground-truth ones. Our experiments show how Zero-Shot-BERT-Adapters outperforms various baselines in two zero-shot settings: known intent classification and unseen intent discovery. The proposed pipeline holds the potential for broad application in customer care. It enables automated dynamic triage using a lightweight model that can be easily deployed and scaled in various business scenarios, unlike large language models. Zero-Shot-BERT-Adapters represents an innovative multi-language approach for intent discovery, enabling the online generation of novel intents. A Python package implementing the pipeline and the new datasets we compiled are available at the following link: https://github.com/GT4SD/zero-shot-bert-adapters.