Verse 31 is a statement that gives an update on the church's growth.
# the church throughout all Judea, Galilee, and Samaria
This is the first use of the singular "church" to refer to more than one local congregation. Here it refers to all the believers in all the groups throughout Israel.
# had peace
"lived peacefully." This means the persecution that started with the murder of Stephen was finished.
# was built up
The agent was either God or the Holy Spirit. This can be stated in active form. AT: "God helped them grow" or "the Holy Spirit built them up" (See: [[rc://en/ta/man/translate/figs-activepassive]])
"Walking" here is an idiom for "living." AT: "living in obedience to the Lord" or "continuing to honor the Lord" (See: [[rc://en/ta/man/translate/figs-idiom]]).
This is an generalization for Peter's visiting the believers in many places in the region of Judea, Galilee, and Samaria. (See: [[rc://en/ta/man/translate/figs-hyperbole]])