Article on port, town in Hampshire (7)
I believe the answer is:
Here is my best explanation:
'town in hampshire' is the definition.
(I've seen this before)
'article on port' is the subsidiary indication.
'article' becomes 'an' (example of the part-of-speech).
'on' is a charade indicator (letters next to each other).
'port' becomes 'dover'.
(Other definitions for andover that I've seen before include "Hants town", "Hampshire town", "New town development" and "Town in Hampshire".)