Person that's good and mature presented in theatre (6)
I believe the answer is:
staged
'presented in theatre' is the definition.
(presented on a stage)
'person that's good and mature' is the wordplay.
'person that's good' becomes 'st' (abbreviation for saint).
'and' means one lot of letters go next to another.
'mature' becomes 'aged' (similar in meaning).
'st'+'aged'='STAGED'
(Other definitions for staged that I've seen before include "Put on play or other performance" , "Orchestrated" , "Get ads (anag) - performed" , "Put on as theatre would" , "Organised (a performance)" .)