follow through (on/with sth)
phrasal verbwithfollowverbuk/ˈfɒləʊ/us
(alsofollow sth through (with sth))to do something as the nextpartof anactivityorperiodofdevelopment:
Given thesuccessofourinitiative, wedecidedtofollowit through withfurtherinvestment.
He was taken tocourtbecause hefailedtofollowthrough with apaymentplanfor thetaxesheowedfor 1999 through 2004.