Amongst layered materials, transition metal dichalcogenides (TMDs) are studied extensively due to their complex phase diagrams exhibiting competing phases. Intercalation provides unique insight into the ground state of the TMDs, by changing the ground states already at low intercalation levels. We propose muon spin rotation experiments in Co1/3NbS2, a novel intercalated TMD system exhibiting a rich phase diagram and a probable Kondo spin liquid state at high pressures. Whereas Co1/3NbS2 was originally found to order antiferromagnetically at 26 K, our specific heat, magnetization, and transport experiments show that the ordering possesses uncommon magnetically fluctuating and field-dependent properties with two separate ordering temperatures of T1= 26 K and at T2=23 K.