If I don't fail, I'll be able to get my driver's license by the end of the year.
Literal
Fail-[if-ば] not, this-year within driver's-license [subject-が] take-can.
落ちる here means 'fail [a test],' its specific use in the school/test context. 落ちなければ is the ~ば conditional negative. 今年中 ('within this year') marks a temporal scope; 中 ('inside / within') attaches to time periods to mean 'within.' 取れる is the potential of 取る.