Adding fence section on 45 degree angle
The vinyl fence has proprietary hardware for attaching the panels. If you can determine the brand and source parts, I'm sure they'll have skewed connectors for you.
Otherwise, get your carpentry on. Rip the edge off a panel at a 45 degree angle using a table saw or a circular saw with a clamped board as a guide. Mount the uncut edge to the new post per the hardware manufacturer's instructions, and mount the cut edge to the existing post with countersunk corrosion-resistant screws. Optionally add vinyl screw caps to pan-head screws.
You've asked a broad question, so I'm only able to provide a general answer. If you like, revise your post with more detail and ask a more specific question.