Most gym bags are made from nylon and polyester textiles. These synthetics are made from petrochemicals and are non-biodegradable as well, so they are inherently unsustainable on two counts. Nylon manufacture creates nitrous oxide, a greenhouse gas 310 times more potent than carbon dioxide. Making polyester uses large amounts of water for cooling, along with lubricants which can become a source of contamination. Both processes are also very energy-hungry.
If in good condition, take your pre-loved gym bag to a secondhand/charity shop.
Please keep from landfill as long as possible.