Convict's first connection in prison (5)
I believe the answer is:
clink
'prison' is the definition.
(the clink can informally mean prison)
'convict's first connection' is the wordplay.
'convict's first' becomes 'c' (lst letter of 'convict').
'connection' becomes 'link' (link is a kind of connection).
'c'+'link'='CLINK'
'in' acts as a link.
(Other definitions for clink that I've seen before include "Rattle of coins; prison (slang)" , "Old London prison" , "Ringing sound - prison" , "Prison - knock glasses together" , "Sound made when hitting glass" .)