The phrase "to follow through on" means to complete or finish something that you have started or promised to do. It means taking action and doing what you said you would do. Full definition
If one of you doesn't follow through on promises to do your share of the work around your home, try and discover together why there is such reluctance. (thespruce.com)
He also made chronically poor staff choices and his office was notorious for not following through on promises and proposals. (timesunion.com)
But far too many artists email me and tell me that they want to sell their art — but then don't follow through on what they know they need to be doing. (theabundantartist.com)