Newspaper beginning to blush at woman’s figure on the beach (9)
I believe the answer is:
sunbather
'figure on the beach' is the definition.
(someone sunbathing on the beach)
'newspaper beginning to blush at woman's' is the wordplay.
'newspaper' becomes 'sun' (UK newspaper The Sun).
'beginning to' indicates taking the first letters.
'woman's' becomes 'her' (belonging to a woman).
The first letter of 'blush' is 'b'.
'sun'+'b'+'at'+'her'='SUNBATHER'
(Other definitions for sunbather that I've seen before include "One trying to get brown" , "One hoping for a tan" , "Loafer on the beach" , "One enjoying holiday" , "Tanner" .)