Hi,
There is an easy method to get private keys from your wallet on "Trust Wallet" app if addresses were imported. You can find it on "Settings" of your wallet.
For account created there, you have your answer on
official "Trust Wallet" website:
Yes! You and only you control the private keys in your Trust Wallet.
Your private keys (all derived from your recovery phrase) never leave the Trust Wallet app. The only way to get them out is when you reveal the recovery phrase. So handle it with great care!
No-one, not the Trust Wallet team, not the backend, not any of the DApps or other mobile apps, no-one can access to the private keys from your wallet. Whenever an operation is needed that requires the private key, Trust Wallet only signs a message with the private keys, without revealing it.
Your recovery phrase is the master password for the private keys. If you have different currencies (BTC, ETH, BNB, etc.) in your multi-coin wallet, each has a different private key internally, all derived from the recovery phrase. Is is possible to recover these private keys? Trust Wallet does not support extraction of the internal private keys, but they are derived from the recovery phrase using industry-standard methods, also used by other wallets (there are even some tools for deriving the private keys off a recovery key, such as iancoleman.io/bip39 28).
So, you can't export your private key but theoretically, could exist other methods to get it using some tools. But I'm not sure you can use iancoleman.io at the moment to do it.
If you want to recover your wallet, you can use your seed. Or may be you can import your wallet created there on Electrum via your seed and export the private key from there (if you are talking about BTC adress off course).
And yes, Binance is a good and reputable exchange but, from the first sentence of your post, you need to know that Binance has been hacked too. On Internet, there are no guaranties...