STO has a few ramp ups in difficulty. It occurs roughly once every 10 levels, but those are petty gentle increases. Those are really meant to test your understanding of the ship's capabilities and bridge officer abilities.
The big jumps in difficulty happen when you start playing Delta Rising missions. From here on, the game starts throwing curveballs at you with every enemy having different strengths to be countered and weaknesses to be exploited. Off the top of my mind, here are a few examples...
* Vaadwaur have nasty long-range artillery that take a few seconds to activate but can one-shot most ships. So you have to constantly move your ship at top speed to avoid those big red circles.
* Iconians have a bunch of gateways that either summon more Iconian ships or cause massive damage but have very low hitpoints. So you have to prioritize destroying gateways asap.
* Tzenkenthi ships have insane bonuses when they are close together, their cruisers buff nearby ships, but they have weak forward shields. So you must make sure you never bunch them together with Gravity Wells, always target their cruisers first and attack them from the front.
* Hur'q swarmers love to attack you from behind, so escorts who use cannon weapons will need to figure out a way to either shake them loose or somehow quickly turn around to engage them. Most other ships have a slightly easier time handling the swarmers with beam fire at will or using mines.
Also... If you can post your ship build, we can take a look and suggest potential ways for easy improvements to your ship.