settle an old score

settle an (old) score (with sb) AND settle old scores (with sb) (to do something bad to someone because they did something bad to you) — сводить (старые) счeты, отплатить за (старые) обиды, расквитаться

Example 1: I have a score to settle with him — У меня с ним свои счеты.

Example 2: In his new autobiography, Klein settles old scores by taking shots at many of his colleagues.

Example 3: ...enemies who have an old score to settle

pay off / wipe off an (old) score (with sb)

Synonyms or related words:
pay back
get back at
get one's own back (on sb) ({mainly BrE, infml} (to do something bad to someone in return for harm they have done to you; to get revenge)

Example 1: I'll get my own back on him one day, I swear! — Клянусь, я ему (за все) отомщу. Я с ним за все расквитаюсь. Он мне за все заплатит.

Example 2: He was bitter, determined to get his own back. (MM)

get / be even (with sb)
hit back

respond in kind (to behave to someone in the same way that they have behaved to you)

revenge oneself on sb (for sth)/ be revenged on sb (for sth)