Here the word "we" refers to Paul and those who oppose the circumcision of Christians. He is probably including the Galatians. (See: [[rc://en/ta/man/translate/figs-inclusive]])
Possible meanings are 1) "we are waiting by faith for the hope of righteousness" or 2) "we are waiting for the hope of righteousness that comes by faith."
"We wait with excitent" or "we wait with great desire"
# for the hope of righteousness
They confidently expect that God will make them righteous. Alternate translation: "for the righteousness that we hope for" or "for the righteousnss that we confidently expect to receive"