Very fine polymath finally getting BA? (8)
I believe the answer is:
hairline
'very fine' is the definition.
(I've seen this before)
'polymath finally getting ba?' is the wordplay.
'finally' says to take the final letters.
'getting' means one lot of letters go next to another.
'ba?' becomes 'airline' (British Airways).
The final letter of 'polymath' is 'h'.
'h'+'airline'='HAIRLINE'
(Other definitions for hairline that I've seen before include "Natural margin on the head (that recedes)" , "Barnet's border" , "Very narrow opening" , "Type of crack" , "area on the outskirts of Barnet?" .)