The star is upset by what anonymous letters may contain (7)

I believe the answer is:

threats

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'anonymous letters may contain' is the definition.
I can't judge whether this definition defines the answer.

'the star is upset by' is the wordplay.
'is upset by' indicates anagramming the letters.
'the'+'star'='thestar'
'thestar' with letters rearranged gives 'THREATS'.

'what' is the link.

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(Other definitions for threats that I've seen before include "Sources of danger -- shatter (anag)" , "Shatter (anag) - menaces" , "Terrifying demands" , "Statements of intentions to harm" , "Expressions of intention to harm" .)

I've seen this clue in The Irish News.

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