She remains a bit of a lady (4)

I believe the answer is:

isla

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'bit of a lady' is the definition.
'isla' can be an answer for 'lady' (I've seen this before). I am not sure about the 'bit of a' bit.

'she remains a' is the wordplay.
'she remains' becomes 'isl' (I can't justify this - if you can you should give a lot more credence to this answer).
'isl'+'a'='ISLA'

Can you help me to learn more?

(Other definitions for isla that I've seen before include "Woman" , "Scottish lady" , "Girl" , "lady from Scotland" , "Lisa (anag.), another girl's name" .)

I've seen this clue in the Evening Standard.

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