Goat god longing to show spirit (7)
I believe the answer is:
panache
'spirit' is the definition.
(thesaurus)
'goat god longing' is the wordplay.
'goat god' becomes 'pan' (I've seen this before).
'longing' becomes 'ache' (I've seen this before).
'pan'+'ache'='PANACHE'
'to show' acts as a link.
(Other definitions for panache that I've seen before include "A dashing manner" , "Flamboyant confidence" , "'Dash, flair (7)'" , "Flamboyant self-assurance" , "Sense of style, swagger" .)