Grant a privilege to zabbix user for "SHWO SLAVE STATUS"
If you can capture SQL Error Message, then you might see the message as below.
2017-01-01 01:01:01 zabbix[zabbix] @ localhost [] ERROR 1227: Access denied; you need (at least one of) the SUPER, REPLICATION CLIENT privilege(s) for this operation : SHOW SLAVE STATUS
You can check the privileges as below.
SELECT USER, HOST, SUPER_PRIV, REPL_CLIENT_PRIV
FROM mysql.user
WHERE USER = 'zabbix';
Then you need to update the privileges.
Method #1. GRANT. (Recommendation)
GRANT REPLICATION CLIENT ON *.* TO 'zabbix'@'localhost';
GRANT REPLICATION CLIENT ON *.* TO 'zabbix'@'127.0.0.1';
Method #2. UPDATE.
UPDATE mysql.user
SET
REPL_CLIENT_PRIV = 'Y'
WHERE USER = 'zabbix';
Now, check the privileges again.
SELECT USER, HOST, SUPER_PRIV, REPL_CLIENT_PRIV
FROM mysql.user
WHERE USER = 'zabbix';
That's it.