I want to transfer my character from one gamertag on the ps4 to another new gamertag on the same console, is this possible?
I'm afraid this is not possible, no. Your progress is irrevocably locked to the specific gamertag you made that progress on, and can not be transferred to another gamertag, like you would be able to with just transfering to another console.
Quoting from Rockstar Support:
"When transferring from PlayStation3 to PlayStation4, you must use the same PSN ID. A new PSN ID on PlayStation4 cannot be transferred to from a different PSN ID on PlayStation3 since your characters progress is tied to the PSN account."