Letter given to speaker's investigator in government department (9)
I believe the answer is:
exchequer
'government department' is the definition.
(I've seen this before)
'letter given to speaker's investigator' is the wordplay.
'letter' becomes 'ex' (X**).
'given to' is a charade indicator (letters next to each other).
'speaker's' indicates a 'sounds like' (homophone) clue.
'investigator' becomes 'checker' (checker is a kind of investigator).
'checker' sounds like 'chequer'.
'ex'+'chequer'='EXCHEQUER'
'in' is the link.
(Other definitions for exchequer that I've seen before include "large supply of money" , "Government coffers" , "old government office" , "Purse" , "Department in charge of a nation's finances" .)