You only need 3 members to be in clan wars and gain xp. to gain xp towards your clan all you have to do is play with at least 1 other member of your clan! each member you play with will get 50xp towards your clan if you win and 10xp if you lose! if you have 4 members you can also play clan vs clan and receive 400xp for every win! all you have to do is play any regular match online as well!
You gain clan Xp for playing multiplayer with at least one other clan member. And you can do this with just 2 people in your clan. To participate in clan wars you need at least 3 members and for clan v clan 4 members.
See #9 in this thread that lays out how to earn XP.
9) How does my clan earn XP?
You can earn Clan XP 3 different ways in Ghosts:
1) Play any multiplayer game mode with 1 or more clan members (must be at least 2 clan members)
A Win = 50 Clan XP per clan member in the lobby
A loss = 10 Clan XP per clan member in the lobby
2) Participate in the Clan vs Clan mode
A Win = 100 Clan XP per clan member in the lobby(400 XP Total)
A Loss = 20 Clan XP per clan member in the lobby(80 XP Total)
3) Participate in the Clan Wars mode
Clan Wars may eventually have some final rewards at the end of the War where your clan receives some Clan XP but otherwise the only Clan XP you may earn is from playing with clan members in the multiplayer game modes.
Clan Ops and Clan Challenges are gone. They were part of COD Elite which is for BO2/MW3 and Ghosts is using an entirely new system.