Shichibukai As A Team
The terms that the Shichibukai are on with each other is best described as very unstable. They practically have very little if any respect for each other and will for the most part not accept help from one another, apparently from a firm sense of pride. During the battle meeting for the Shichibukai where only two members are absent it is even stated that the very notion of them working together as a team is entirely unthinkable. However Kuma and Doflamingo don't disregard the notion of teaming up with another Shichibukai. Kuma offered Moria help defeating the Strawhats and Doflamingo offered Crocodile a chance to team up. However both refused the offer due to their pride.
How To Become A Shichibukai
Any pirate can choose to join the Shichibukai if a space becomes open . However, in order for one to become a Shichibukai once this position opens up, one must be able to show their strength against other pirates while choosing to pledge loyalty to the World Government by making a pact with the top leaders. Once they become renowned, the position may be offered to them, if no other pirate has accepted the position or proven to be more of an asset to the World Government. As expected, most members were already notorious pirates with high bounties, but even unknown pirates can be admitted if they accomplish some feat to prove their strength, such as defeating someone with a world-wide known strength like when Blackbeard beat Ace and turned him in to the government.
(defeated by Monkey D. Luffy, status revoked)
Dracule Mihawk (Hawk Eyes)
(active, secretly working against the government)
(active, turned into a cyborg)
Blackbeard (Marshall D. Teach)
(take the position after Crocodile defeat. Traitor, now on the loose)
(traitor, now on the loose)
(betrayed by the marines, he managed to escape)
(set in prison after being defeated by Luffy, he's now on the loose)
(Allied with the Straw Hat Pirates, Status revoked)
Buggy the Star Clown