So this issue has now been resolved. Following was completed to add the link to Link controller
* Create the new vlan
* Create Self IPs
* Create a node on LTM module for the new Internet router
* Create the new link in GTM module and assign big_ip monitor
But after doing this even though the node in LTM module is up and there is fill connectivity between F5 and new Internet router, Link in GTM module wont come up. But as soon as I added the link IP address to out default pool(one that is being referred in default route), link in GTM module came up.
But thanks everyone for their help.