Log Shipping with Clustered Instance- back up Current Set up- Clustered Instance Active/Passive
Node  -1
Node  -2
Current Back ups goes to Network Drive
Cluster Drive

E drive

Virtual Name ABC
Shared Folder - e\Share

New instance- for Log Shipping

My question is if i set up a log shipping between clustered instance will it break my current back ups that goes to the network
Not at all. You can continue to have the backups on the FCI go to your network share. The log shipping job can be configured to copy from the network share to a local drive on the new instance, or read right from the network share.