Answered by Shaykh Faraz Rabbani
Is it permissible to pray istikhara while having many (years) missed prayers that one has to make up?

Assalamu alaikum wa rahmtullah,
Yes, it remains permitted to perform sunnas such as istikhara when there is need or benefit.
Please see the following related SunniPath answer:
Makeup Prayers: Can I leave the confirmed Sunnas?
Jazakum Allahu Khayr
Wassalam
Faraz Rabbani