Steady girlfriend who may be a Londoner (6)

I believe the answer is:

sedate

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'steady girlfriend who may be a londoner' is the definition.
'sedate' can be an answer for 'steady' (thesaurus). I'm not sure about the remainder of the definition.

'steady girlfriend' is the wordplay.
'steady' becomes 'se' (I can't justify this - if you can you should believe this answer much more).
'girlfriend' becomes 'date' (date can mean someone you are dating).
'se'+'date'='SEDATE'

Can you help me to learn more?

(Other definitions for sedate that I've seen before include "boring" , "Calm - staid" , "Staid; put to sleep" , "Calm or spectral appartition" , "Dignified and subdued" .)

I've seen this clue in The Independent.

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