It'll start right back up again completely naturally as soon as you stop taking the pills. The pills are hormone blockers. The gonads still produce sex hormones, but the blockers react with the hormones and render them inert. The inert hormones are passed as urine like any other waste product in the blood. A few days after you stop taking the blockers, they'll run out and the sex hormones will start expressing themselves just like they would in someone who never took the blockers. Puberty will begin (or resume) just as nature planned.
The only side effect is that you won't go through puberty. Unfortunately, this does mean you'll have a child's amount of bone density, which is not good for a lifetime. But there's absolutely 0 risk in delaying puberty until age 18. You'll just grow up slower, the same as any late bloomer.
Hormone blockers are actually a component in an adult trans person's hormone replacement therapy. To take me as an example, I have a pair of testes which produce testosterone. So I take an antiandrogen; a testosterone blocker, to suppress the effects. And I take estrogen pills so that I have a female blood chemistry. When I started taking hormone pills, my body reacted just like any teenage girl's body. I got softer skin, mood swings, and better hair. I tell you what, having the emotions of a teenage girl as an adult is an absolute trip. I'm glad they've settled down since then. Some trans women I know even got period cramps, despite not having a uterus. I don't envy them.
The body is genetically programmed to respond to sex hormones in a certain way. It doesn't matter what you were born as, everyone's organs, muscles, bones, and brain have a genetic programming that responds to estrogen one way, and testosterone another way. The potential is already inside every living human. That potential remains there for your entire life. Puberty blockers can't do anything to take it away.
If I ever stopped taking my testosterone blocker, I'd start growing bigger muscles and hair in strange places. My body would resume functioning like a male body. One day I'll get my testes removed, and I'll never have to worry about that again. But that surgery is only available to adults, and it requires a psychiatric assessment. I've been openly trans for years and years and I'm still not allowed to do it yet. There's absolutely no risk of a child going through the procedure without the absolute greatest caution, and a very urgent, life-saving need. And even if a horrible one in a billion mistake was made, they could just give the kid hormone pills the same as I take in order to restore their original sexual chemistry.