en_tn/pro/20/07.md

walks in his integrity

Here walking refers to living. See how you translated this phrase in Proverbs 19:1. AT: "lives by his integrity" or "lives an honest life" (See: rc://en/ta/man/translate/figs-idiom)

his sons who follow after him

This simply means that they "follow after him" since they are younger than he and his children. If this phrase is awkward in your language it may be left to be implied. AT: "his sons after him" or "his sons" (See: rc://en/ta/man/translate/figs-explicit)