RobH_en_tn/act/20/24.md

if only I may finish the race and complete the ministry that I received from the Lord Jesus

This speaks about Paul's "race" and "ministry" as if they are objects that Jesus gives and Paul receives. Here "race" and "ministry" mean basically the same thing. Paul repeats this for emphasis. Alternate translation: "so that I may complete the work that the Lord Jesus has commanded me to do" (See: rc://en/ta/man/translate/figs-metaphor and rc://en/ta/man/translate/figs-doublet)

finish the race

Paul speaks about completing the work that Jesus has commanded him to do as if he were running a race. (See: rc://en/ta/man/translate/figs-metaphor)

to testify to the gospel of the grace of God

"to tell people the good news about God's grace." This is the ministry that Paul received from Jesus.