Set off towards that woman carrying publicity to Foreign Office (4,3)

'set off towards that woman' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'publicity to foreign office' is the wordplay.
I cannot really see how this works, but
'publicity' could be 'ad' (advert) and 'ad' is found within the answer.
'to' could be 'for' and 'for' is located in the answer.
The remaining letters 'he' is a valid word which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).

'carrying' acts as a link.

Can you help me to learn more?