Curlynursern

Yes, you need a new needle. This is the rule for any procedure you will do as a nurse where you are "inserting" anything. (IV, needle for a blood draw, port needle, foley..) — with IVs and blood draws, you can adjust the angle without pulling the needle out of the skin... but once the needle is out; you have to start over. Since ports are accessed at a 90 degree angle you have no choice but to start from scratch.  There is no readjusting without removing the needle entirely.
Infection prevention is a major goal of care obviously, but ESPECIALLY with sterile procedures like accessing a port, foley insertion, etc. you will see nurses miss the urethra and reinsert the same foley; don't be that nurse. Leave it in place so you know where not to go and grab another kit.

Ports are central venous access— potentially introducing bacteria to a major blood vessel is a recipe for disaster. Not to mention, most people who have ports have compromised immune systems to begin with. 
The outside of the skin is sterile before you break the skin— because you've cleaned it using sterile technique prior to accessing. If you miss the port; you've broken the skin barrier in that location ( so the needle is no longer sterile— it has touched parts of the body that were not sterilely prepped). you have to remove the needle and repeat the entire sterile process—- grab a new kit, apply new sterile  gloves (the outside of the package for a new port needle is not sterile, so your gloves would no longer be sterile once u went to open it)  use alcohol and chlorhexidine to clean the area again, —- and go for it w/ the new needle.
Hope that helped! If you're not yet solid/confident on port accessing protocol, definitely have a nurse educator review with you/demonstrate for u, and then access a port with them present. first several times you do this you should take someone more experienced and ideally more qualified with you to make sure you're following protocol. It's easy to slip up and become unsterile if you're not doing it routinely. I'm on an onc floor and while I take care of many patients w/ ports, I don't access them all that regularly, so I always take someone with me
Sooooo, anyways, I gave the long winded version ……but to answer directly, Yes u definitely most certainly need a new needle! Stay curious / keep asking questions.