The quickest way of syncing Parity Ethereum client with the top of the chain is achieved using Warp sync in combination with
To make sure you get the most recent snapshot available and warp sync very close to the top of the chain, Parity Ethereum >=v1.10.1 supports the flag
--warp-barrier [NUM]. Replace
[NUM] with the chain's latest block number minus at least 10,000 blocks. Example: if latest block number is 5,633,123 you should launch parity
$ parity --warp-barrier 5620000
I recommend this parameter
$ parity --pruning fast --jsonrpc-interface all --jsonrpc-hosts all --warp-barrier 5620000
Ref: How to get Parity Ethereum in sync quickly?