Going out of turn, Peter can make a name (6)
I believe the answer is:
repute
'a name' is the definition.
(name can mean someone's reputation)
'going out of turn peter' is the wordplay.
I cannot quite see how this works, but
'turn' could be 'u' (a 'U-turn' is a kind of turn) and 'u' is present in the answer.
an anagram of 'peter' is 'repte' which is present in the left over letters.
This accounts for all the letters.
This explanation may well be incorrect...
'can make' is the link.
Can you help me to learn more?
(Other definitions for repute that I've seen before include "State of high regard" , "credit" , "Distinction" , "State of high esteem" , "Generally held opinion" .)