To be a great powerlifter or strongman, you must have great lockout strength. And the same exercises that build lockout strength are also great for triceps size. Example: Partial pressing movements with a variety of positions/grips.
Here are a few that’ll have a profound effect on your triceps size and ability to press a shit-ton of weight. Heavy-partials done off pins, or floor presses, work well for this, and they’re great for developing absolute strength:
Dead Stop Floor Press
Use standard bar or a football bar (as shown) for a neutral grip. Brace and press. Add accommodating resistance if you’d like (chains or bands).
Dead Stop Press Off Pins
Set the pins high enough that you’re working just the top half.
Close-Grip Fat Bar Dead-Press Against Doubled Mini-Bands
For an extra challenge, use a fat bar and attach bands.
Seated Safety Squat Bar Press Off Pins
This overhead press will challenge your triceps, grip, and forearms because of the awkwardness of the bar.
Some of the variations here allow accommodating resistance. If you’re able to, use it to get even more variability in your training, not to mention the benefit of maximal tension when you’re strongest – at lockout. But it’s certainly not a requirement. By that same token, specialty bars are not needed either.
You need your presses done from a dead-stop, no bouncing off the pins. Use a moderate or close grip, and perform this work for maximal effort, building to a 1-5 rep max. This work should take place first in your upper-body training session.