From what I remember, Jellico is a rear admiral, lower half (one-star) in command of Deep Space 5 in 2373 in Star Trek: New Frontier and the next appearance of him was as an admiral (of indeterminate stars) serving at Starfleet Headquarters in 2379 during Star Trek: A Time to...; based on him becoming the Commander-in-Chief of Starfleet in 2380, I lean toward him being a full four-star admiral in 2379. And, of course, he resigned his post and retired in the aftermath of Star Trek: Destiny in 2381, and I imagine him living out his civilian life with his children and/or grandchildren ever since.
Oh, as I'm writing this, it's coming back to me that in 2376 (the Deep Space Nine: Relaunch era) that Cmdr. Vaughn doesn't particularly care for Jellico, and I think Vaughn mentioned that he was back on Earth (or at least a notable member of the admiralty) at the time.
So, Jellico probably spent some or all of the War at Deep Space 5 before being kicked upstairs to Starfleet Headquarters.