Not a new teacher, but costs a lot to obtain nowadays (3,6)
I believe the answer is:
old master
'not a new teacher but costs' is the definition.
I can't tell whether this defines the answer.
'a lot to obtain nowadays' is the wordplay.
'a lot' means to remove the first letter (I've seen 'a lot of' mean this).
'to obtain' becomes 'hold' (synonyms).
'nowadays' becomes 'master' (I can't explain this - if you can you should give a lot more credence to this answer).
'hold' with its first letter removed is 'old'.
'old'+'master'='OLD MASTER'
Can you help me to learn more?
(Other definitions for old master that I've seen before include "work of art" , "Classic painting" , "scholar with greybeard" , "soon to retire from school?" , "Great painter of former times - or one of his works" .)