Many everyday tasks cannot be accomplished without adequate grip strength, and corticomotor drive to the spinal motoneurons is a key determinant of grip strength. In persons with tetraplegia, damage to spinal pathways limits transmission of signals from motor cortex to spinal motoneurons. Corticomotor priming, which increases descending drive, should increase corticospinal transmission through the remaining spinal pathways resulting in increased grip strength. Since the motor and somatosensory cortices share reciprocal connections, corticomotor priming may also have potential to influence somatosensory function. The purpose of this study was to assess changes in grip (precision, power) force and tactile sensation associated with two different corticomotor priming approaches and a conventional training approach and to determine whether baseline values can predict responsiveness to training. Participants with chronic (≥1 year) tetraplegia (n = 49) were randomized to one of two corticomotor priming approaches: functional task practice plus peripheral nerve somatosensory stimulation (FTP + PNSS) or PNSS alone, or to conventional exercise training (CET). To assess whether baseline corticospinal excitability (CSE) is predictive of responsiveness to training, in a subset of participants, we assessed pre-intervention CSE of the thenar muscles. Participants were trained 2 h daily, 5 days/week for 4 weeks. Thirty-seven participants completed the study. Following intervention, significant improvements in precision grip force were observed in both the stronger and weaker hand in the FTP + PNSS group (effect size: 0.51, p = 0.04 and 0.54, p = 0.03, respectively), and significant improvements in weak hand precision grip force were associated with both PNSS and CET (effect size: 0.54, p = 0.03 and 0.75, p = 0.02, respectively). No significant changes were observed in power grip force or somatosensory scores in any group. Across all groups, responsiveness to training as measured by change in weak hand power grip force was correlated with baseline force. Change in precision grip strength was correlated with measures of baseline CSE. These findings indicate that corticomotor priming with FTP + PNSS had the greatest influence on precision grip strength in both the stronger and weaker hand; however, both PNSS and CET were associated with improved precision grip strength in the weaker hand. Responsiveness to training may be associated with baseline CSE.