Inserting a SD card does not change the phone's "Internal" storage. It just adds "External" storage. Meaning you can move files, music, etc., not apps, to the card. To actually have the card add space the apps can use you would need to change the card over to "Internal" storage. If possible on that device that is. The following are the instructions on how it is done.
First, you need to be using a phone that is running at least Android "Marshmallow" (6.0) or newer, or be able to upgrade to it. Second, you will need the instructions I am including below. And third, you need a phone that has not been restricted by the manufacturer from making this change. Which does happen.
NOTE: If any of the steps are missing on your phone, or they don't work for you, then you have a phone that either has an older Android version or has been restricted by the manufacturer. If that is the case, you will not be able to use this information.
How to turn the "External" SD card into "Internal" storage - Option A
NOTE: Please be sure you start with a blank SD card. It needs to be blank because when the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device).
1. Go to device “Settings”, then select “Storage”.
2. Select your "SD Card", then tap the “three-dot menu“ (top-right), now select “Settings” from in there.
3. Now select “Format as internal”, and then “Erase & Format”.
4. Your SD Card will now be formatted as internal storage.
5. Reboot your phone.
NOTE: If you don't reboot the phone, many things may not work correctly, so make sure you do.
How to turn the "External" SD card into "Internal" storage - Option B
IMPORTANT NOTE: Be sure you start with a blank SD card. When the card is converted to "Internal" storage, it will be formatted (wiped) and encoded (making the cards data only readable by that device), so anything on it prior would be gone.
1. Go to "Settings", and then select "Storage & USB".
2. At the bottom of the list you should see the SD card's details, including the option to format it and make it "Internal" storage.
3. Once this is done, reboot the device and you can start running things from the card.
NOTE: If you don't reboot the phone, some things may not work correctly, so make sure you do the reboot.
A Final Note: If you set up the card as "Internal" storage, then the data on it will not be readable by any other device. To access the data you would have to connect he phone to say a computer and copy it over to the computer from the phone/card. Otherwise only phone can read the data. Also, be sure you do not reset (hard or factory) the phone. If you do, then all the data on the card will no longer be readable, even by the phone itself.