You control the miners in the private network, so you just need to customize them to accept transactions with gasPrice = 0.
From the Parity documentation:
--gasprice WEI Minimum amount of Wei per GAS to be paid for a
transaction to be accepted for mining. Overrides
Note that this doesn't change how gas itself works in the network. You still have gas limits and can generate out of gas errors. The only difference is that the client is saying it will pay 0 for gas on a transaction and the miner is staying it is willing to accept transactions at 0 price.
Or if using GETH
$ geth --networkid 29462 --datadir "./data" --gasprice 0 --nodiscover --port 31313