Abstract: Cross-lingual transfer (XLT) driven by massively multilingual language models (mmLMs) has been shown largely ineffective for low-resource (LR) target languages with little (or no) representation in mmLM's pretraining, especially if they are linguistically distant from the high-resource (HR) source language. Much of the recent focus in XLT research has been dedicated to \textit{LR language families}, i.e., families without any HR languages (e.g., families of African languages or indigenous languages of the Americas). In this work, in contrast, we investigate a configuration that is arguably of practical relevance for more of the world's languages: XLT to LR languages that do have a close HR relative. To explore the extent to which a HR language can facilitate transfer to its LR relatives, we (1) introduce Karde\c{s}-NLU, an evaluation benchmark with language understanding datasets in five LR Turkic languages: Azerbaijani, Kazakh, Kyrgyz, Uzbek, and Uyghur; and (2) investigate (a) intermediate training and (b) fine-tuning strategies that leverage Turkish in XLT to these target languages. Our experimental results show that both - integrating Turkish in intermediate training and in downstream fine-tuning - yield substantial improvements in XLT to LR Turkic languages. Finally, we benchmark cutting-edge instruction-tuned large language models on Karde\c{s}-NLU, showing that their performance is highly task- and language-dependent.