Mad tea party host is a milliner (6)
I believe the answer is:
hatter
'a milliner' is the definition.
('hatter' can be a synonym of 'milliner')
'mad tea party host' is the wordplay.
I cannot quite understand how this works, but
'tea' could be 't' (I've seen this in other clues) and 't' is found within the answer.
The remaining letters 'hater' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'is' acts as a link.
Can you help me to learn more?
(Other definitions for hatter that I've seen before include "Threat (anag)" , "Tea party participant (Alice)" , "supplying pork pies?" , "Topping chap" , "Tea-party holder" .)