This paper considers a localized data-driven consensus problem for leader-follower multi-agent systems with unknown discrete-time agent dynamics, where each follower computes its local control gain using only their locally collected state and input data. Both noiseless and noisy data-driven consensus protocols are presented, which can handle the challenge of the heterogeneity in control gains caused by the localized data sampling and achieve leader-follower consensus. The design of these data-driven consensus protocols involves low-dimensional linear matrix inequalities. In addition, the results are extended to the case where only the leader's data are collected and exploited. The effectiveness of the proposed methods is illustrated via simulation examples.