You can. If you have provided the ability for such a migration. Some addOldData(...) method. Or if there is no migration method, then, may be, you can repeat all requests - same as to previous contract. Or, may be in old contract you have getData() method - then you can call it from new contract or from application level.
If no options above are not available for you, then create a new contract with these methods and deploy it again.
In a worst case, if you have much of data in old contract and no methods to gain the data - you still can obtain them by other means - tools (libs) for blockchain analisys. All the contract's data are public, so it should be possible.