Search for a particular string in Oracle clob column

select *  
from TABLE_NAME
where dbms_lob.instr(COLUMNNAME,'searchtext') > 0;

Below code can be used to search a particular string in Oracle clob column

select *  
from RLOS_BINARY_BP
where dbms_lob.instr(DED_ENQ_XML,'2003960067') > 0;

where RLOS_BINARY_BP is table name and DED_ENQ_XML is column name (with datatype as CLOB) of Oracle database.

ok, you may use substr in correlation to instr to find the starting position of your string

select 
  dbms_lob.substr(
       product_details, 
       length('NEW.PRODUCT_NO'), --amount
       dbms_lob.instr(product_details,'NEW.PRODUCT_NO') --offset
       ) 
from my_table
where dbms_lob.instr(product_details,'NEW.PRODUCT_NO')>=1;

Use dbms_lob.instr and dbms_lob.substr, just like regular InStr and SubstStr functions.
Look at simple example:

SQL> create table t_clob(
  2    id number,
  3    cl clob
  4  );

Tabela zosta│a utworzona.

SQL> insert into t_clob values ( 1, ' xxxx abcd xyz qwerty 354657 [] ' );

1 wiersz zosta│ utworzony.

SQL> declare
  2    i number;
  3  begin
  4    for i in 1..400 loop
  5        update t_clob set cl = cl || ' xxxx abcd xyz qwerty 354657 [] ';
  6    end loop;
  7    update t_clob set cl = cl || ' CALCULATION=[N]NEW.PRODUCT_NO=[T9856] OLD.PRODUCT_NO=[T9852].... -- with other text ';
  8    for i in 1..400 loop
  9        update t_clob set cl = cl || ' xxxx abcd xyz qwerty 354657 [] ';
 10    end loop;
 11  end;
 12  /

Procedura PL/SQL zosta│a zako˝czona pomyťlnie.

SQL> commit;

Zatwierdzanie zosta│o uko˝czone.
SQL> select length( cl ) from t_clob;

LENGTH(CL)
----------
     25717

SQL> select dbms_lob.instr( cl, 'NEW.PRODUCT_NO=[' ) from t_clob;

DBMS_LOB.INSTR(CL,'NEW.PRODUCT_NO=[')
-------------------------------------
                                12849

SQL> select dbms_lob.substr( cl, 5,dbms_lob.instr( cl, 'NEW.PRODUCT_NO=[' ) + length( 'NEW.PRODUCT_NO=[') ) new_product
  2  from t_clob;

NEW_PRODUCT
--------------------------------------------------------------------------------
T9856