Popular organisation, though old-fashioned, is swamped (9)
I believe the answer is:
inundated
'swamped' is the definition.
(synonyms)
'popular organisation though old-fashioned' is the wordplay.
'popular' becomes 'in' ('in' can mean trendy).
'organisation' becomes 'UN' (the United Nations is an organisation).
'though old-fashioned' becomes 'dated' (dated can mean old-fashioned. I am not sure about the 'though' bit.).
'in'+'un'+'dated'='INUNDATED'
'is' is the link.
Can you help me to learn more?
(Other definitions for inundated that I've seen before include "drowned" , "flooded" , "Deluged" .)