Show amusement with gym-goer discontented at home (4)
I believe the answer is:
grin
'show amusement' is the definition.
(I've seen this in another clue)
'goer discontented at home' is the wordplay.
'discontented' says to hollow out the word (remove centre letters) (the word's contents are removed).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'goer' with its middle removed is 'gr'.
'gr'+'in'='GRIN'
'with gym' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for grin that I've seen before include "Beam" , "A broad smile showing the teeth" , "Facial expression, usually of pleasure" , "Accept with good grace - . . . . and bear it" , "Smile broadly showing teeth" .)