From monarch +‎ -ical, perhaps after Middle French monarchique.^[1]

• (UK) IPA^(key): /məˈnɑːkɪk(ə)l/

• Audio (Southern England):

  (file)

monarchical (not comparable)

1. Of or pertaining to a monarch or monarchy.

   Although a socialist he did have monarchical leanings

2. Having sole or undivided authority.
   • 2009, Diarmaid MacCulloch, A History of Christianity, Penguin, published 2010, pages 133–4:

     But in this contest of martyrs, it was Ignatius's passionate account of a monarchical episcopal ministry which set the pattern for the future.

• monarchal, monarchial, monarchic