Tight sort of fleece given to female dressing (9)

I believe the answer is:

skinflint

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'tight sort' is the definition.

'fleece given to female dressing' is the wordplay.
'fleece given' becomes 'skin' (I've seen this in other clues. I am not sure about the 'given' bit.).
'to female' becomes 'f' (common abbreviation).
'dressing' becomes 'lint' (I've seen this before).
'skin'+'f'+'lint'='SKINFLINT'

'of' is the link.

Can you help me to learn more?

(Other definitions for skinflint that I've seen before include "Niggard, scrooge" , "21 [MISER]" , "Scrooge, miser" , "A miserly person like Scrooge" , "A miserly person, tightwad" .)

I've seen this clue in The Telegraph.

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