"I think it's time we cleared the air, don't you?" What does that mean? "we cleared" and "don't you" in one sentence... How's that possible?
It's not only possible, Smarty, it's exceedingly common in English. These are called tag or mini questions. We use them not so much to ask a real question, but to seek confirmation or agreement where we already have some knowledge of a situation or the answer is what the speaker sees as the expected answer.
As a full question, it would be,
"Don't you think it's time we cleared the air?"
Some more examples of tag/mini questions:
1. You like [+] pizza, don't [-] you?
2. You don't [-] like broccoli, do [+] you?
We NORMALLY use a negative tag with a positive statement [see 1.] and a positive tag with a negative statement [see 2.]
In 1, the tag question is framed with a positive statement because there is an expectation that what the speaker wants or expects is a 'yes' reply.
In 2, the tag question is framed with a negative statement because there is an expectation that what the speaker wants or expects is a 'no' reply.
This doesn't mean of course, that the answer will/must be the expected one.
It's gonna rain, isn't it?
Moscow is in Russia, isn't it?
Putin is Russia's leader, isn't he?
Gorbachev isn't Russia's current leader, is he?
Australia isn't in the Northern Hemisphere, is it?
We can make tag/mini questions out of any real question.