We got this error when granting permissions for one of our new slave server (it could be for an ordinary MySQL server, too):

Error 'Your password does not satisfy the current policy requirements' on query. Default database: ''. Query: 'GRANT REPLICATION SLAVE ON *.* TO 'reusr'@'127.0.01''

It appeared that MySQL has activated by default a password checking plugin and our password in the GRANT (or SET PASSWORD) option didn’t meet the requirements.
So here is what you can do:

OPTION 1) Lower the password policy level

Check the policy level and lower it if it is MEDIUM or HIGH (they are there options LOW=0, MEDIUM=1 the default and HIGH=2). The policy level controls how to check and what is involved in the complexity algorithm for the passwords. More details here – https://dev.mysql.com/doc/refman/5.7/en/validate-password-options-variables.html#sysvar_validate_password_policy. Here is what you have:

[myuser@mysql1 ~]# mysql
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 13
....
....
mysql> SHOW VARIABLES LIKE 'validate%';
+--------------------------------------+--------+
| Variable_name                        | Value  |
+--------------------------------------+--------+
| validate_password_check_user_name    | OFF    |
| validate_password_dictionary_file    |        |
| validate_password_length             | 8      |
| validate_password_mixed_case_count   | 1      |
| validate_password_number_count       | 1      |
| validate_password_policy             | MEDIUM |
| validate_password_special_char_count | 1      |
+--------------------------------------+--------+
7 rows in set (0.00 sec)

So set the validate_password_policy=0 and try again your query:

mysql> set global validate_password_policy=0;
Query OK, 0 rows affected (0.00 sec)

If you still get the error your password is lower than the validate_password_length (=8 by default) so you need to change it at last to 8 characters. But what if you what zero password (or with 1,2,3 characters)? Setting validate_password_length to 0 won’t work, because there is a hard limit to 4, so you cannot set it to 0 event the set query is not reporting error when using 0 with validate_password_length.

You should uninstall the plugin.

OPTION 2) Uninstall the MySQL Validation Plugin

You can uninstall the validation plugin on-the-fly in a working server without restarting or reloading and then you can set whatever password you like.
Here is how to do it:

[myuser@mysql1 ~]# mysql
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 13
....
....
mysql> UNINSTALL PLUGIN validate_password;
Query OK, 0 rows affected (0.03 sec)

mysql> SHOW VARIABLES LIKE 'validate%';
Empty set (0.01 sec)

As you can see no “validate_password” variables are available anymore! Now set your password.
But there is a catch, if you have started the server with “–validate-password=FORCE_PLUS_PERMANENT” (you can check it with “ps axuf|grep mysqld” in the command line) you won’t be able to uninstall the plugin live even with the root MySQL user. So at the end if you do not have root permissions to restart the MySQL service without this option it might be better to change your password or skip the query if it is received by the slave in the MySQL replication bin log.
You can install the plugin again with:

[myuser@mysql1 ~]# mysql
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 13
....
....
mysql> INSTALL PLUGIN validate_password SONAME 'validate_password.so';
Query OK, 0 rows affected (0.00 sec)

And it will be available over restarts, too, because it is registered in “mysql.plugin” table.