Q: If the amount has been debited into accrued expenses, do we need to credit it after making the payment (so that the balance would be zero in accrued expenses)?
A: Accrued Expenses is a liability account. It is not an expense. Accrued means "is/are owed" or "owing".
Therefore, when you record an expense owing, you do the following: Dr Expense Cr Accrued Expenses (liability account)
When you make the payment you record: Dr Accrued Expenses Cr Bank
Apart from when you're making a payment to the creditor, a debit to the accrued expense account is highly unusual and would mean a correction to how much is owed to the creditor. It would mean you owed the creditor less. The entries above are the standard, usual entries for owing a creditor and then paying off the debt.