The RAISERROR command in your trigger raises an error with a user defined number. This error is not a standard SQL error, but RAISERROR can still be done in SQL2012.

The trigger tests for the value of some inserted fields and an error is raised if a NULL value is entered. You could replace this functionality by adding constraints to the table. Just make the appropriate columns NOT NULLABLE. It depends on your application if it can handle the different approach on this NULL-value checking. You have to test this for yourself.

The last part of the trigger is checking for inserted values in another table. This could be replaced by defining a foreign-key relation between both tables.

So if you replace the functionality of the trigger by other ways (described above) you probably are able to completely remove the trigger. But this has to be tested to know for sure.