Convict in trouble over prison term initiated by judge (8)
I believe the answer is:
jailbird
'convict' is the definition.
(synonyms)
'trouble over prison term initiated by judge' is the wordplay.
'trouble' becomes 'ail' (synonyms).
'over' means one lot of letters go next to another (in a down clue, some letters go over others).
'prison term' becomes 'bird' (bird can mean time served in prison).
'initiated by' says to put letters next to each other (some letters go at the start of others).
'judge' becomes 'J' (abbreviation for judge).
'ail' next to 'bird' is 'ailbird'.
'ailbird' put after 'j' is 'JAILBIRD'.
'in' is the link.
(Other definitions for jailbird that I've seen before include "Convict" , "Old lag" , "Habitual prisoner" , "Criminal who has been incarcerated repeatedly" .)