LotR -- Book 5 - Chapter 07 - The Pyre of Denethor

[Zigûr]

I always assumed Gandalf "gave" Imrahil command fairly informally; Imrahil seems to have been wise enough to have recognised Gandalf's good sense, and as Formendacil has said, he alone needed to be convinced, perhaps even just informed; Imrahil was (by position at least) possibly the second most important man in Gondor after Denethor himself.

(Prince of Dol Amroth seems to have been one of the highest positions in the realm; his ancestor had been "chief" of Cirion's companions at the swearing of the Oath of Eorl, and one of only four men (along with Cirion and Eorl themselves, and Eorl's own Chief Captain Éomund) who decided on the boundaries of Rohan.)

It was probably Imrahil's responsibility in the chain of command to take charge at that point, and simply needed someone better-informed than himself at that time, who he respected, to tell him that he needed to take on that role.