Can I trade right away with funds from a closed trade in my IRA?

You can request an upgrade from a Cash account to a Margin account while tagged as having been Free Riding in Client Portal, as described in Client Portal Users' Guide…

When you open a margin account you have the ability to borrow from IBKR. You can not set a limit or a set only a specific amount of margin to use in a margin account. If the account has sufficient Available Funds then a new order would be accepted. There is a calculated margin requirement for positions in a margin type account displayed as an Initial margin and Maintenance margin requirement. In addition to contracts traded in the account any borrowed cash from Forex trading or from trading outside the account’s Base Currency can have a calculated margin requirement. There are tools available so you can monitor your account’s margin requirements and cash balances in real time or as a daily snapshot…

To trade using unsettled funds, you need to upgrade your account from a 'Cash' type to a 'Margin' type. A margin account allows you to use unsettled funds for trading purposes, providing more flexibility in your trading activities. Here is what you need to know:…

As the assets in an IRA account are not eligible to be pledged as loan collateral, and stock ordinarily serves as the collateral securing payment of a margin loan, account holders are not permitted to buy stock on margin in either a Cash or Margin type IRA account. All stock purchases must be paid for in full with cash.  In addition, other transactions which require a margin account such as shorting stock and selling uncovered options are not allowed in either a Cash or Margin type IRA account…