`gzip` nowadays can compress files larger than 4 GiB in size, and in fact doesn’t have any limit of its own really (you’ll be limited by the underlying file system). The only limitation with files larger than 4 GiB is that `gzip -l`, in version 1.11 or older, won’t report their size correctly; see Fastest way of working out uncompressed size of large GZIPPED file for an alternative. This has been fixed in `gzip` 1.12; `gzip -l` decompresses the data to determine the real size of the original data, instead of showing the stored size.
There are many other compression tools which provide better compression and/or speed, which you might find more appropriate: XZ, 7-Zip...