If the Tarpon swims parallel to the beach you can get him on the reel you have, you can walk after him.
If the Tarpon swims away from the beach you will need more line.
Have another Rod with a heavy duty Spro ball bearing snap swivel that will fit thru all the guides and put a 6/0 on it.
Only fill the 6/0 three quarters of the way.
If the Tarpon is stripping you on your casting reel, tie a surgeons knot into the line and after you clip the surgeons knot loop with the snap swivel and fight the fish on the 6/0.
Helps to have someone help you, but if you have the second rod at hand rigged and ready you can do it all yourself.
RedHeaded Fella did this for a guy who was being stripped by a big Tarpon on Frisco Pier back in the day, the Tarpon had run under the pier and the fisherman was pinned to one railing on the North Side and the Tarpon was headed South. Someone snagged the line with the Tarpon on it on the South side, Redheaded Fella tied the lines together and after the original rod was cut loose the fisherman went on to fight the Tarpon for another hour or so. Fisherman actually left the pier and followed the Tarpon on the beach. A guy on the Pier held the rod and dropped it down to the fisherman when he got on the sand. Tarpon was about 150 pounds or so. Redheaded fella was known for stuff like that.
There were more Tarpon hooked up on Frisco on the OBX than the other piers.
More Tarpon the further South you go.