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A is a partner in a partnership and has $10,000 in her capital account. Her share of the 2021 partnership income is $3,000. To add the $3,000 to A's capital account what is the journal entry?

It's done through two journal entries. Let's say that the total partnership revenue is $10,000, total expenses are $4,000, and A and B split income and losses 50%/50%:

Journal Entry 1 - To close out the temporary revenue/expense accounts to income summary.

Debit - Revenue 10,000
Credit - Expenses 4,000
Credit - Income Summary 6,000

Journal Entry 2 - To allocate income/losses to the partners' capital accounts.

Debit - Income Summary 6,000
Credit - Capital, Partner A 3,000
Credit - Capital, Partner B 3,000

Are you saying to debit each specific revenue account and credit each expense to zero out the balance?

Yes. You're closing out all of the temporary revenue/expense accounts to Income Summary and then closing out Income Summary to adjust each partner's capital account. At the close of each accounting period, the balances of all of the income/expense accounts and Income Summary should be zero.

Moat accounting systems close all these accounts to a retained earnings account. Then, the entry to make is the following Jan 1 to close out retained earnings and distribute among the capital accounts of partners