How to Update an old theme for the latest wordpress version

WordPress is exceptionally backwards compatible, so it is typical even for older themes to just work for a long time.

However for solid results you would want to perform several meaningful actions:

  1. Straight up code review, if your experience and time allows. Just read through all of the code, gauge if it makes sense.

  2. Running through everything with WP_DEBUG enabled. Straight errors will come up, but also any formally deprecated functions/features will emit warnings with suggestions to update.

  3. Run through Theme Check plugin and see what comes up. You don’t necessarily want to bother with all of that for custom theme, but it’s a good to see what’s up.

  4. If you customize theme for private use — make a proper fork of it, changing name and details. Otherwise you risk invalid update from the repo destroying your changes. However do keep proper attribution to original author for copyright/licensing reasons.