Cutting wood, a popular apprentice (7)
I believe the answer is:
trainee
'apprentice' is the definition.
(I've seen this in another clue)
'cutting wood a popular' is the wordplay.
'cutting' means one lot of letters goes inside another (some letters cut their way into a word).
'wood' becomes 'tree' (I can't explain this - if you can you should give a lot more credence to this answer).
'popular' becomes 'in' ('in' can mean trendy).
'a'+'in'='ain'
'tree' going around 'ain' is 'TRAINEE'.
Can you help me to learn more?
(Other definitions for trainee that I've seen before include "One undergoing instruction" , "21 [TYRO]" , "one needs to practice" , "Student" , "novice" .)