Crossword Genius

Times going after Foreign Office and Chancellor – they're out for blood? (3-4)

Ross

I believe the answer is:

fox-hunt

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'out for blood?' is the definition.
The definition suggests a singular noun which matches the answer.

'times going after foreign office and chancellor' is the wordplay.
'times' becomes 'x' (x resembles the multiplication or times sign).
'going after' says to put letters next to each other.
'foreign office' becomes 'FO' (abbreviation).
'and' means one lot of letters go next to another.
'chancellor' becomes 'hunt' (I can't explain this - if you can you should give a lot more credence to this answer).
'x' put after 'fo' is 'fox'.
'fox'+'hunt'='FOX-HUNT'

'they're' acts as a link.

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I've seen this clue in The Guardian.
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