Martin n'est pas arrivé depuis longtemps.

Bonjour Martin, The tricky issue here is that you can't use the verb "to arrive" the same way as we use "arriver" in French. In this context, you'd rather use "to be" in English, however you need to remember that "arriver" in French is more of a process (i.e. in bad English it would be closer to "Martin hasn't got/arrived there for long"). Therefore, here, the process of "getting there" IS finished in the past, and NOT ongoing in the present: that's why you need to use Le Passé Composé. FYI, "Martin n'arrive pas depuis longtemps." would give a very weird "Martin hasn't been getting there for long.", giving the impression that he's still in the process of arriving! I hope that's helpful!