Yes there is, and it is already in place. There has been bipartisan oversight of intelligence from Congress for decades. A subset of the people's representatives with the necessary security clearances make sure that there are no Deep State shenanigans. Yes, it failed in the run up to the Iraq invasion, but it worked for decades before, during the Cold War.
- Partisanship in Congress has resulted in a government so dysfunctional that it's been shut down. We can't trust people who can't even keep the government running to watch over services so accustomed to keeping everyone in the dark.
- The committee may have been effective during the cold war but in recent times, the NSA was engaged in mass surveillance for while this committee was in place and it took an internal whistleblower for it to come to light.
- The head of the NSA lied to Congress. The oversight committee can't oversee if they can't get the truth.
You might be able to argue that this is a solution but you most definitely cannot argue that it's a good solution when it's recently been proven to be ineffective.