Digger covers for sick hatter (8)
I believe the answer is:
milliner
'hatter' is the definition.
(I know that hatter can be written as milliner)
'digger covers for sick' is the wordplay.
'digger' becomes 'miner' (I've seen this in another clue).
'covers' means one lot of letters goes inside another.
'for sick' becomes 'ill' (I can't justify this - if you can you should give a lot more credence to this answer).
'miner' going around 'ill' is 'MILLINER'.
Can you help me to learn more?
(Other definitions for milliner that I've seen before include "Garment maker" , "Maker and seller of hats" , "Philip Treacy, say" , "One making pork-pies" , "Women's hat maker" .)