Firm desire to go back after that rabbit (5)

'rabbit' is the definition.
('coney' can be a synonym of 'rabbit')

'firm desire to go back after' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'desire' becomes 'yen' (yen is a kind of desire**).
'to go back' says the letters should be written backwards.
'after' means one lot of letters go next to another.
'yen' in reverse letter order is 'ney'.
'co'+'ney'='CONEY'

'that' acts as a link.