Your extension will only be issued up to the validity of the passport so, in your case 6 months, then you apply for a new 12 month extension for your new passport, you lose 6 months.
Just get your father to apply online for a Non-O retirement (over 50) Visa as he will then not require proof of onward travel at check in, gets stamped in for 90 days and does not need to visit Immigration at all during his stay. The UK cost is £60 then nothing more to pay (the online TDAC arrival card is free).