Prerequisites

The trigger must be in your own schema or you must have ALTER ANY TRIGGER system privilege.

In addition, to alter a trigger on DATABASE, you must have the ADMINISTER DATABASE TRIGGER privilege.

CREATE OR REPLACE
  TRIGGER TEST_TRG
    AFTER CREATE
    ON DATABASE
BEGIN
    NULL;
END;
/

SQL> select banner from v$version;

BANNER
--------------------------------------------------------------------------------
Oracle Database 12c Enterprise Edition Release 12.2.0.1.0 - 64bit Production
PL/SQL Release 12.2.0.1.0 - Production
CORE    12.2.0.1.0      Production
TNS for 64-bit Windows: Version 12.2.0.1.0 - Production
NLSRTL Version 12.2.0.1.0 - Production

SQL> show user
USER is "U1"
SQL> select privilege from user_sys_privs order by 1;

PRIVILEGE
----------------------------------------
ADMINISTER DATABASE TRIGGER
ALTER ANY TRIGGER
CREATE SESSION

SQL> alter trigger scott.test_trg disable;
alter trigger scott.test_trg disable
              *
ERROR at line 1:
ORA-01031: insufficient privileges


SQL>

SQL> select banner from v$version;

BANNER
--------------------------------------------------------------------------------
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
PL/SQL Release 12.1.0.2.0 - Production
CORE    12.1.0.2.0      Production
TNS for 64-bit Windows: Version 12.1.0.2.0 - Production
NLSRTL Version 12.1.0.2.0 - Production

SQL> show user
USER is "U1"
SQL> select privilege from user_sys_privs order by 1;

PRIVILEGE
----------------------------------------
ADMINISTER DATABASE TRIGGER
ALTER ANY TRIGGER
CREATE SESSION

SQL> alter trigger scott.test_trg disable;

Trigger altered.

SQL>