Is it obligatory to perform the 'Aqeeqah for a newborn while there is a debt that cannot currently be paid?

Slaughtering the Aqiqah (definition) is only a Sunnah (definition) and not obligatory. If it is possible to combine settling the debt and offering the Aqiqah, that is better. However, if it is not possible to combine them, then prioritizing the debt, which is a right of others, is more obligatory than slaughtering the Aqiqah. If the debt is settled, the Aqiqah can be offered for the newborn as long as they have not reached puberty. If they reach puberty, the responsibility for it falls away from their guardian and becomes their own.