Hi Ake Hae,
'더 한국어를 공부해야지요.' is supposed to be '한국어를 더 공부해야지요.' to be in right order.
And '한국어 공부를 더 해야죠' may sound more natural.
It means 'I need to study Korean more.'
(Because the subject is not specified, I suppose it is 'I'.)
Also, you can also say '한국어 공부를 더 열심히 해야죠' for 'I need to study Korean harder.'
Hope it helps.