These two phrases refer to the same thing. They are repeated to show the seriousness of God's promise to Abraham. (See: [[rc://en/ta/man/translate/figs-parallelism]])
# to grant to us
"to make it possible for us"
# that we, having been delivered ... would serve him without fear
"hand" refers to the control or power a person. This could be stated clearly. AT: "from the control of our enemies" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This can be restated to remove the abstract nouns "holiness" and "righteousness." Possible meanings are 1) we would serve God in holy and righteous ways. AT: "doing what is holy and righteous" or 2) we would be holy and righteous. AT: "being holy and righteous" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])