Here is a link.
https://emrtds.nepalpassport.gov.np/
Passport renewal application should be available throughout the year.
Figure out if there is a branch consulate nearby where you can apply in person. Otherwise, you will have to carefully read the instructions on the website and mail the instructed materials to the processing center. Make sure you use mail/courier service with a tracking number.
They will never answer your phone calls in a million years. Email also, I don't think they will ever commit to that extra responsibility or tasks they choose not to handle even if they fall under their regular job duties. The current embassy in DC was at least neat, clean, and organized when I last visited. Their previous office had unimpressive furniture and ambience and whole place looked like a "kiraanaa pasal godaam" office in the southern border of Nepal. Some officers were very eager to help you out while the clerks acted as if they wished you had never shown up there. That's me speaking in a formal attire and putting on a most courteous demeanor in years.
This is Nepal society represented by a consular office in not just an OECD country but a superpower nation. Good luck.