SQL> CREATE DATABASE LINK testlink
  2  CONNECT TO xxmitg IDENTIFIED BY ******
  3    USING 'GITGD';

Database link created.

SQL> create table test
  2  (
  3  a integer
  4  );

Table created.
--connect to other database
SQL> conn xxmitg/******@gitgd

SQL>  create table test
  2   (
  3   a integer
  4   );

Table created.
---connect to first database
SQL> conn ayush/pass

SQL> select * from test@testlink;

no rows selected



SQL>  CREATE or REPLACE TRIGGER testtrigger
  2   after insert on test
  3   FOR EACH ROW
  4   
  5   declare
  6   v_int number;
  7   
  8   begin
  9   select a into v_int from test@testlink where  a=:new.a;
 10   exception
 11   when NO_DATA_FOUND  then
 12   insert into test@testlink values(:new.a);
 13   end;
 14   /

Trigger created.

SQL> select * from test;

no rows selected

SQL> select * from test@testlink;

no rows selected

SQL> insert into test values(1);

1 row created.

SQL>  select * from test;

         A
----------
         1

SQL> select * from test@testlink;

         A
----------
         1