Countess’s foremost milliner linked to TV gossip (10)
I believe the answer is:
chatterbox
'gossip' is the definition.
(I've seen this before)
'countess's foremost milliner linked to tv' is the wordplay.
'foremost' indicates taking the first letters.
'milliner' becomes 'hatter' (synonyms).
'linked to' is a charade indicator (letters next to each other).
'tv' becomes 'box'.
The first letter of 'countess' is 'c'.
'c'+'hatter'+'box'='CHATTERBOX'
(Other definitions for chatterbox that I've seen before include "talk show star, potentially?" , "Windbag" , "One using plenty of gas" , "Gossip" , "Bletherer" .)