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Hi, Does I need to see the phrase "As was her status as the heir apparent" like was before it the word "If" ?
I hope you got my point ... because it seems that that was something that she wasn't "heir apparent" right?

"Although Clinton hadn’t yet formally declared her intention to enter the race,
in political circles it was seen as a foregone conclusion, (If) as was her status as the heir apparent,
the prohibitive front-runner-in-waiting. And that was making many Democrats distinctly nervous in the
summer of 2006."
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as was ~ and so was ~ and ... was also

Although Clinton hadn’t yet formally declared her intention to enter the race,
in political circles it was seen as a foregone conclusion,
as was her status as the heir apparent,
~ and so was her status as the heir apparent,
~ and her status as the heir apparent was also seen as a foregone conclusion
the prohibitive front-runner-in-waiting.

Compare:

The ability to speak Chinese was important for the ambassador, [as was / and so was] the ability to write it.
..., and the ability to write Chinese was also important.

Your greeting card was very much appreciated, [as was / and so was] the little gift you included inside.
..., and the little gift you included inside was also very much appreciated.

You can do this in any tense. Here's one in the present tense:

Meryl Streep is an Oscar nominee this year, [as is / and so is] Brad Pitt.
..., and Brad Pitt is also an Oscar nominee this year.

CJ
Comments  
FlowersaDoes I need to see the phrase
Do I need to see the phrase...
Flowersa (If) as was her status as the heir apparent
No, "if" is neither needed nor allowed here. The sentence is saying that both Clinton's intention to enter the race and her status as the heir apparent were equally clear (they were both "foregone conclusions" i.e.there was no doubt about either).

Remember that in 2006 Clinton had not yet become yesterday's news, she was still a hot item in the Democrat Party's machinery.
 CalifJim's reply was promoted to an answer.