In most cases, you can use Ethereum contracts on Klaytn without any modification. However, be aware of the following two issues.
Klaytn officially supports Solidity v0.4.24 and v0.5.6. These two versions have been thoroughly tested. Other versions should run without any issues, but we still highly recommend using those two versions.
Klaytn decouples key pairs from addresses. If user updates account, the private key for a specific account is replaced with another one. Most cases this will not affect your business logic. However if your business logic includes ecrecover, you should consider using validateSender. For more details, refer to here.