Criminals slow to break into American offices abroad (10)
I believe the answer is:
consulates
'offices abroad' is the definition.
(diplomatic offices)
'criminals slow to break into american' is the wordplay.
'criminals' becomes 'cons' (short for convicts).
'slow' becomes 'late' (I've seen this in another clue).
'to break into' means one lot of letters goes inside another (inserted letters break into the word).
'american' becomes 'US' (United States).
'late' put into 'us' is 'ulates'.
'cons'+'ulates'='CONSULATES'
(Another definition for consulates that I've seen is " diplomats in these".)