You probably need to bend your pins back. Cleaning it alone won't work the pins have been bent, which is super common after pushing the cart down all of these years. You can Google YouTube videos about how to do this.
Replacing the pint connector is an option, but it's difficult finding replacements that are not Chinese junk. If you replace it a poor quality replacement, it will only fail again, but much sooner than your original. Whether you bend your pins back or replace the connector, I would suggest never pushing the game down again. This will hopefully make the pins last longer before they fail again.
Another option is to use a Game Genie. If your pins are clean, but still bent, the Game Genie might make contact because the pins on the GG are thicker than an original game. I don't recommend this option as a permanent solution because it doesn't fix the actual issue. But it can sometimes help as a short term solution.
The best solution in my opinion is to buy a Blinking Light Win and install it. It replaces the pin connector with a more traditional set of pins (not a ZIF connector) and you never have push the dame down again. It requires taking your NES apart, but it's a "bolt on" installation meaning you can always remove it and put your NES back to original if you want. That's what I'm currently using.
EDIT: The Blinking Light Win appears to be sold out at the moment, but it looks like they are taking pre-orders for the next batch. I still recommend this solution, and maybe try to temporarily use a Game Genie for the time being.