At South Ken, they're of use to outgoing mothers (7)
I believe the answer is:
museums
'at south ken' is the definition.
I can't tell whether this defines the answer.
'of use to outgoing mothers' is the wordplay.
I cannot really understand how this works, but
an anagram of 'use' is 'seu' which is located in the answer.
'mothers' could be 'mums' (mum is a kind of mother) and 'mums' is located in the remaining letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'they're' is the link.
Can you help me to learn more?
(Other definitions for museums that I've seen before include "Louvre and V&A?" , "Places like the V&A" , "Sue's mum (anag.)" .)