Port gives mother a bad character (9)
I believe the answer is:
rotterdam
'port' is the definition.
(I've seen this before)
'mother a bad character' is the wordplay.
'mother' becomes 'rotter' (synonyms).
'a bad character' becomes 'dam' (I can't justify this - if you can you should believe this answer much more).
'rotter'+'dam'='ROTTERDAM'
'gives' is the link.
Can you help me to learn more?
(Other definitions for rotterdam that I've seen before include "city abroad" , "Dutch city and port" , "foreign city" , "One of the world's largest ports" , "European city" .)