Have him come early tomorrow morning.

Literal

Tomorrow [possessive-の] morning, him [to-に] early come-receive do.

A complex 'have someone do' construction: 彼にきてもらう = 'receive from him the act of coming' = 'have him come.' The ~てもらう auxiliary marks a favor the speaker receives. Then ~てくれ adds another layer — the plain imperative of くれる, meaning 'do [this] for me.' Stacked together: 'please make it so that he comes early (for me).' The てくれ form is markedly masculine and gruff.