Partitioning with AUTO_INCREMENT primary key
Simply put, you need to put entry_ts in the PRIMARY KEY before you can partition the table.
The table needs to look like this:
CREATE TABLE `TABLE` (
  `HEADER_ID` int(11) NOT NULL AUTO_INCREMENT,
  `STATUS` int(11) NOT NULL DEFAULT '0',
  `CREATED_AT` varchar(45) NOT NULL,
  `TYPE` varchar(45) NOT NULL,
  `VERSION` varchar(45) NOT NULL,
  `ID` varchar(45) NOT NULL,
  `ORIGIN` varchar(45) NOT NULL,
  `PAYLOAD` json NOT NULL,
  `ENTRY_TS` datetime NOT NULL',
  PRIMARY KEY (`HEADER_ID`,`ENTRY_TS`)
);

So, run this:
ALTER TABLE `TABLE`
    DROP PRIMARY KEY,
    ADD PRIMARY KEY (`HEADER_ID`,`ENTRY_TS`);

Then, you can partition the table since ENTRY_TS is part of the PRIMARY KEY.
ALTER TABLE TABLE
    PARTITION BY RANGE(MONTH(entry_ts)) (
    PARTITION JANUARY VALUES LESS THAN (2),
    PARTITION FEBRUARY VALUES LESS THAN (3),
    PARTITION MARCH VALUES LESS THAN (4),
    PARTITION APRIL VALUES LESS THAN (5),
    PARTITION MAY VALUES LESS THAN (6),
    PARTITION JUNE VALUES LESS THAN (7),
    PARTITION JULY VALUES LESS THAN (8),
    PARTITION AUGUST VALUES LESS THAN (9),
    PARTITION SEPTEMBER VALUES LESS THAN (10),
    PARTITION OCTOBER VALUES LESS THAN (11),
    PARTITION NOVEMBER VALUES LESS THAN (12),
    PARTITION DECEMBER VALUES LESS THAN (13)
    );

Please try this in Staging with an empty table.
GIVE IT A TRY !!!