Slate and pine - that's style (7)
I believe the answer is:
panache
'style' is the definition.
('panache' can be a synonym of 'style')
'slate and pine' is the wordplay.
'slate' becomes 'pan' (I've seen this before).
'and' is a charade indicator (letters next to each other).
'pine' becomes 'ache' ('ache' can be a synonym of 'pine').
'pan'+'ache'='PANACHE'
'that's' is the link.
(Other definitions for panache that I've seen before include "Great style" , "stylish carriage" , "Swagger; theatricality" , "Dashing style" , "Flamboyant confidence" .)