Is there any Special rule or Permission for doing Arbitrage? /

There are several types of arbitrage. None of them is possible manually.

So you need permission to fully automated trading on exchanges to be able to write the programs that can detect arbitrage opportunities. Also, you will need lowest latency access to the exchage servers.

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Someone told me there is no need of any permission.

I am sure some procedure is required if you want to do “Fully” automated trading as an individual.

If you are doing manually, no need of any permission. It is fully legal.
But you should be very quick, the price difference would become narrow once your entered the trade.