Well, if the new phone can take the same size (physical dimensions and amount of storage) as the other phone, and the card was left as as when you plugged it to the original phone (and not converted into "Internal" storage), then you should be able to just take it out of one phone and plug it into the other one.
If for some reason the new phone doesn't accept it, or asks to format it. First, don't. That will wipe it all off. If that is the case (or it doesn't read it) then put it back in the original device and then you can either upload all the file to a Google account, or connect the original phone to a computer via USB cord and move the files from the card to an empty folder on the computer. Then, once done insert the card into the new phone, then you can either then download the files from Google to the new device, or connect the new device to the computer via USB cord and move the file over to the card.