Ben is becoming a noted Norwegian (5)
I believe the answer is:
ibsen
'a noted norwegian' is the definition.
'ibsen' can be an answer for 'norwegian' (I have seen 'famous Norwegian' mean 'ibsen' so perhaps 'norwegian' could also mean 'ibsen'). I am unsure of the 'a noted' bit.
'ben is becoming' is the wordplay.
'becoming' indicates anagramming the letters.
'ben'+'is'='benis'
'benis' with letters rearranged gives 'IBSEN'.
Can you help me to learn more?
(Other definitions for ibsen that I've seen before include "Noted Norwegian playwright" , "See 7 Down" , "Playmaker" , ""Doll's House" dramatist" , "Norse playwright" .)