Here "chains" refers to Paul's being arrested and put in prison. AT: "people will put me in prison and cause me to suffer" (See: [[rc://en/ta/man/translate/figs-metonymy]])
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. AT: "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]])
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]])