To unlock the Clan War trophy in The Division, you don't need to have four or your clan mates together in the match at the same time. You don't need to be facing a team made up of players that are all from the same clan either.
It would appear you need to be a member of a clan, and play a match where at least one member from the opposing team is also the member of a clan.
To join or create a clan, you can follow the instructions for the Strength in Number trophy:
Once you're in a clan, press
to open the map and press
to select the conflicts tab, and select Quickplay. Once the game has loaded, the trophy will unlock if a member of the opposing team has joined a clan.