Surveillance job with second coffee option provides clue to theme (5-3)
'surveillance job' is the definition.
(a stake-out is a surveillance operation)
'second coffee option provides clue to theme' is the wordplay.
I cannot quite understand how this works, but
'second' could be 's' (common abbreviation) and 's' is found within the answer.
'coffee option' could be 'takeout' (coffee might be ordered as take out or takeaway) and 'takeout' is present in the answer.
No letters remain.
This may be the basis of clue (or it may be nonsense).
'with' acts as a link.
(Another definition for stake-out that I've seen is "Police surveillance operation".)