The regular expressions are not right, and the way you've used is pretty cumbersome.
Instead, you can opt to use POSIX character classes. In your specific case, it will be like so:
[[:alpha:]]{4}[[:digit:]]{3}
so the constraint check is
CONSTRAINT Code_Check check (REGEXP_LIKE(Paper_Code,'[[:alpha:]]{4}[[:digit:]]{3}')
This checks that there are 4 alphabetic characters, followed by 3 numeric.
Example on SQL fiddle & more info available at regexp cheatsheet