It's not necessarily a tricep weakness, but this is a common sticking point for a raw lifter.
Other than just getting stronger in general some specific things have helped me with this:
1) Hard arch and a good tight setup, pressing the bar back over the face.
2) Speed benches with band tension. I get a lot out of it, and I tend to smoke a max bench, then add 5 pounds and get crushed.
3) Wider grip benching. In my experience, this tends to force the bar path to the optimal. Move your hands out way wide, it should be uncomfortable, but it will help to build the muscle memory for the bar path.
Tried pin-pressing once for my standing press, but ending up getting weaker over all. If you go that route, maybe add some regular benches in before or after.