Master-slave carrier recovery is a digital signal processing technique that uses correlated phase noise in multi-channel receivers to eliminate redundant carrier recovery blocks. In this paper we experimentally investigate the performance of master-slave carrier recovery for multicore fiber transmission in the presence of inter-channel nonlinear interference. Using a triple parallel loop setup we jointly receive three spatial channels in a 7-core fiber for transmission distances of up to 1600 km. We find that an increased launch power causes a moderate penalty on the slave channels. Furthermore, we study the penalty from a non-zero inter-core skew.