At home, anxious and earnest (7)
I believe the answer is:
intense
'earnest' is the definition.
(I've seen this in another clue)
'at home anxious' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'anxious' becomes 'tense' (I've seen this before).
'in'+'tense'='INTENSE'
'and' acts as a link.
(Other definitions for intense that I've seen before include "Extreme - strong" , "Very marked" , "Set nine (anag.)" , "Feeling deeply" , "Of extreme force" .)