If all the 21 million Bitcoin are already mined, it means there's no more new Bitcoin to release. Which means that miners won't anymore receive block rewards. Bitcoin mining could continue but since there's no more Bitcoin left to mine, what they will receive in return will only be transaction fees. Today, miners receive block rewards and transaction fees. The moment the maximum supply is reached, only transaction fees remain.

The rest, whether it would still be profitable to mine, whether Bitcoin's security would remain intact, whether Bitcoin would finally face its end, and so on we could only speculate. After all, the last Satoshi wouldn't be mined until around the year 2140, long after we're all gone.