See this answer. If there is enough room after the partition then there may be no need to copy files. (1) Use
fdisk or gdisk to remove the partition and to create a new partition with all the same characteristics but the size, the only difference should be the ending sector. Write all the changes at once (i.e. with one w of fdisk/gdisk). This step can be done online, it should not disturb programs using the filesystem. (2) Enlarge the filesystem. This step can or cannot be done online, depending on the filesystem. What is the filesystem?