Is it possible to change the Index of a database table by the following?

I have a mysql table ( tbl_test ) that has a unique ID, string and an int order.

ID | Nome  | Ordem 
1  | name1 |  1 
2  | name2 |  4 
3  | name3 |  3 
4  | name4 |  5 
5  | name5 |  2

I would like to know if it is possible to insert a new new element with order 3 to pass all elements from the old three up one. In other words, when entering 6 | name6 | 3 the table would look like this:

ID | Nome  | Ordem 
1  | name1 |  1 
2  | name2 |  5 
3  | name3 |  4 
4  | name4 |  6 
5  | name5 |  2
6  | name6 |  3