South Bank potentially narrow (7)

I believe the answer is:

slender

I'm a little stuck... Click here to teach me more about this clue!

'potentially narrow' is the definition.
'slender' can be an answer for 'narrow' (similar in meaning). I am not certain of the 'potentially' bit.

'south bank' is the wordplay.
'south' becomes 'S' (synonyms).
'bank' becomes 'lender'.
's'+'lender'='SLENDER'

Can you help me to learn more?

(Other definitions for slender that I've seen before include "Faint" , "Thin or narrow" , "Sylphlike" , "Barely sufficient; thin" , "Svelte" .)

I've seen this clue in The Sun.

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