No. The amount of miners isn't tied to how many bitcoins exist, or how many transactions are happening.
Maybe you're thinking of how when more people are mining, it becomes harder to mine. This is because there is a global fixed rate of Bitcoin creation. Every 10 minutes, 12.5 new bitcoins come into existence. Miners are effectively competing for the chance to be the one to receive those new bitcoins. If mining becomes unprofitable, then some miners will drop out, causing it to become more profitable for those remaining. Miners don't set prices or rules; price affects profitability which either causes more miners to mine or some to drop out.
Maybe you're thinking of how when more people are mining, it becomes harder to mine. This is because there is a global fixed rate of Bitcoin creation. Every 10 minutes, 12.5 new bitcoins come into existence. Miners are effectively competing for the chance to be the one to receive those new bitcoins. If mining becomes unprofitable, then some miners will drop out, causing it to become more profitable for those remaining. Miners don't set prices or rules; price affects profitability which either causes more miners to mine or some to drop out.