Susan James' book 'Kateryn Parr' (the first edition, as opposed to the later edition 'Catherine Parr') has lots of detailed information on Anne and all the Parr family. The later edition still has some, but removed a lot of this.She has a Wikipedia article and, I think, an ODNB article. If you're in the UK, you can access this for free using your library card number.
I can only add that I show her as born in 1514, died in 1552. She is listed as a Maid of Honour in 1543 but as she would have been 29, she was most likely a Lady of the Chamber. She was also referred to as Keeper of the Jewels in 1543. She was married to William Herbert, Earl of Pembroke although I do not have the date of this marriage at hand. Their son, Henry was contracted to marry Katherine Grey. The father forced through a divorce to distance himself from the plot to place Jane Grey on the throne instead of Mary Tudor. William and Ann also had a daughter named Ann.
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