I know both are Gaudiya Vaishnava organisations. But are they related in any way (Guru Parampara etc)?
Both founders of Sri Narasingha Chaitanya Ashram (Swami B.G. Narasimha and Swami B.B. Vishnu) are initiated (dīkṣita) disciples of Srila A. C. Bhaktivedanta Swami Prabhupada, founder of ISKCON. In the Gaudiya Vaishnava tradition coming from Srila Prabhupada Bhaktisiddhanta Sarasvati Thakur, the guru-paramparā is considered a bhāgavata paramparā, where the lineage is not based solely on dīkṣā but on the śikṣā relationship.
To my knowledge, ISKCON has never accepted anyone other than its Founder-Acharya and current members within the institution in the role of śikṣā-guru, and in the years since the departure of the Founder-Acharya has increasingly asserted its identity as an institution with strict boundaries. Many faithful disciples of the Founder-Acharya, Srila A. C. Bhaktivedanta Swami Prabhupada, have found those boundaries redrawn sometimes to their exclusion, and thus have continued on their own, in organizations such as Gaudiya Vedanta Samiti, Sri Chaitanya Saraswata Math, and the numerous Gaudiya Maths. Some disciples of Srila Prabhupada have founded their own organizations, such as Sri Narasingha Chaitanya Ashram, VRINDA, and others.