If it's really 1 mF ( 1000 uF) it's an electrolytic capacitor, which WILL leak ( a few microamps, depending on age, temperature, and bias voltage).

To minimise the leakage it needs to be properly biased (about half its rated voltage) so that the electric field builds up the insulating layer by ... electrolysis. The clue is in its name... If the resulting DC bias is a problem, there are 2 options:

1. A load resistance of a few kilohms will reduce the DC output to a few millivolts
2. Or replace the capacitor with a lower leakage type (film cap or ceramic).

See also this Q&A for more details.

Note there is no need for such a large value : you have 0.22 uF into 0.5 kilohms on the input which will severely limit the LF response. 1000 uF would only be appropriate with a load resistance of a few ohms or less, and the LM833 cannot drive such a low load anyway.

If it's really 1 mF ( 1000 uF) it's an electrolytic capacitor, which WILL leak ( a few microamps, depending on age, temperature, and bias voltage).

To minimise the leakage it needs to be properly biased (about half its rated voltage) so that the electric field builds up the insulating layer by ... electrolysis. The clue is in its name... If the resulting DC bias is a problem, there are 2 options:

1. A load resistance of a few kilohms will reduce the DC output to a few millivolts
2. Or replace the capacitor with a lower leakage type (film cap or ceramic).

See also this Q&A for more details.

Note there is no need for such a large value : you have 0.22 uF into 0.5 kilohms on the input which will severely limit the LF response. 1000 uF would only be appropriate with a load resistance of a few ohms or less, and the LM833 cannot drive such a low load anyway. Your last comment implies it has trouble even driving 100 ohms, which is not very surprising.