1. complete something
follow through on your promise
This expression is most commonly used in relation to completing an activity or process that you have promised that you will do. You follow through with something it means you see something through to completion, you finish it or oversee something being implemented. For that reason, it tends to be more regularly used in a professional environment. To 'follow-through' on something generally has positive connotations, often being associated with discipline, integrity, and hard work.