You can use replace in sql server as below:
declare @strA varchar(50) = '055367911126753316'
declare @strB varchar(50) = '00055367'
select replace(@strA,right(@strB,len(@strB)-2),'')
If it is in different columns in a table you can use as below:
create table #yourcolumns ( cola varchar(50), colb varchar(50))
insert into #yourcolumns (cola, colb) values
('055367911126753316', '00055367')
select replace(cola,right(colb,len(colb)-2),'') from #yourcolumns
I think we need to go for substring in your case as you are looking for startswith
select SUBSTRING(cola,CHARINDEX(LEFT(REVERSE(colb),1),cola)+1,len(cola)) from #yourcolumns