Ask for private trainee (8)
I believe the answer is:
beginner
'trainee' is the definition.
(thesaurus)
'ask for private' is the wordplay.
'ask for' becomes 'beg' (begging is a kind of asking for).
'private' becomes 'inner' (as in one's private or inner thoughts).
'beg'+'inner'='BEGINNER'
(Other definitions for beginner that I've seen before include "One just starting out" , "Tyro, novice" , "Fresher" , "new recruit, perhaps" , "inexperienced person" .)