If you go to ...->about you should see upgrade required if battery is below current version app is looking for - obviously if you are using an old App version, it will only check for latest at that point.
I suspect if you bought a new battery it may even have newer firmware than 1.4 anyway ?
I understood there were issues with older battery firmware so DJI advised not to fly below 1.6? I think, if firmware file is on root of SD card when you power on with each battery it will update if needed (red/green/red/green with beeps), and you will see a new entry in txt file showing firmware upgraded.
This is my old txt file entries from last battery upgrade, the first 'success' is the aircraft and first battery upgrading, the next two 'success' are my 2nd/3rd batteries, then 'firmware identical' is next power up when no update required just so you can see what it will look like.
========== 2014.01.01 00:00:12 remo-con disconnect======
Packet: P3X_FW_V01.06.0040.bin
Upgrading ...
Result: Success.
========== 2014.01.01 00:00:12 remo-con disconnect======
Packet: P3X_FW_V01.06.0040.bin
Upgrading ...
Result: Success.
========== 2014.01.01 00:00:12 remo-con disconnect======
Packet: P3X_FW_V01.06.0040.bin
Upgrading ...
Result: Success.
========== 2016.01.01 15:04:06 =====================
Packet: P3X_FW_V01.06.0040.bin
Result: Abort.
The firmware on the SD card is identical to or older than the current firmware on the aircraft.