Is it necessary to put on a new condom when switching from oral to penetrative sex?
First and foremost, no matter where you started or where you're headed next, if there is ejaculate in the condom, throw it away. Ejaculate can begin to leak out the bottom of the condom and compromise the barrier between partners, which is, obviously, not ideal. So once a condom has been ejaculated in, it's done. Time for retirement. Goodbye forever. Now, say the person wearing the condom has yet to ejaculate. What's the proper condom etiquette for that scenario?
If the penis being stimulated orally is about to be put into a butt or vagina (or another mouth), toss that old condom and put on a fresh one. There's a bunch of reasons to do this, but when it comes to oral sex specifically, teeth (not to mention orthodontic implants, braces, or oral piercings) can easily cause damage to the thin membrane of a condom, and even small tears that aren't obvious at a glance could lead to the condom tearing later.
Regardless of what activities you happen to be switching between, it's always a good idea to swap condoms between acts. It helps prevent accidentally introducing germs to a new part of the body- especially important when transitioning from anal penetration to a new activity. A fresh condom is also freshly lubricated, and less likely to stretch and tear due to increased friction.
Be sure when switching to a new condom that there's no cross contamination. If you're not prepared to get up and wash your hands, designate one partner the condom remover and the other the condom put-er on-er. Teamwork makes the dream work!
So, in conclusion...
Yes! After oral sex, swap out the old condom for a fresh one before moving on to something else.
Always change condoms after ejaculation.
Put on a new condom with clean hands to avoid cross contamination.
Use condom safe lubes to help reduce friction.