I am having the same issue with my figs, the old growth is slow and the newer ones are outgrowing them.

Triple Crown want fruit in South Florida, I live South Georgia want fruit Chill hours to low for that variety.
Tupy best choice for blackberry plant that fruit.

I live in Northeast Oklahoma, and I have six Tripple Crown blackberry plants that I put out two years ago. The first year they didn't do well. Last year after the fruit ripen, the new crowns started growing. In fact, they grew some 25 feet. This year (now) the last years canes have started leaving out and hope they will fruit this year.

I didn't know these blackberries didn't fruit in Florida. I would have thought they would do well down there in the wet humid climate.

I think those old canes should be the fruiting ones this year.They can be tipped,so they produce laterals and bear the fruit.Are they on a trellis?Yeah,your growing seasons are different than mine.Mine are on a two wire trellis and I cut the tips when the cane goes a little over the top one at five feet and then tie it there and then string the laterals from it all along that wire and the lower wire at three feet.These canes can be completely cut off,once they have fruited.
The new canes coming out of the ground will be the fruiting ones for next year.Try to keep these somewhat separate from the older canes.
Gator rider could be right.There may be better varieties for your area. Brady

Most blackberry varieties require some chill hours between 32 and 45 degrees to fruit well. So gator is correct about TC variety and Florida.

Triple Crown is a semi-erect variety, most canes rise at a 30-degree angle, many are much steeper, mine all rise 90 degrees, straight up.

Your above-ground newly sprouted cane is fine, it does not indicate too high a planting. Put some compost around the plant if any roots are showing near the base, this could happen from settling soil after the original planting.

If your original canes are not flowering by July 4, I would give up on them and cut them way back, go with the new growth for berries next year. It can take some time for blackberries to get in sync with the seasons.

Here is some closure to my question. A few weeks after my initial post, the initial sprout (1" up an old cane) took off growing and a few weeks later, sprouts developed on the other two old canes. One sprout was almost 10" up the old cane. Thanks for all your great responses.

In zone 10 this date you should have ripe fruit on any last years canes. I'm telling you this because you now do prune on last years growth may well remove so new growth use energy. Sorry about triple crown not fruiting in your zone wish I could 2 zone lower yours.

The lowest of the Arkansas cultivars is Kiowa, needing only 200 chill hours; Choctaw needs 300; Cherokee needs 500.