follow through (on/with sth)
phrasal verb with follow verb uk/ˈfɒləʊ/ us
(also follow sth through (with sth)) to do something as the next part of an activity or period of development:
Given the success of our initiative, we decided to follow it through with further investment.
He was taken to court because he failed to follow through with a payment plan for the taxes he owed for 1999 through 2004.