Hopefully the "handling" started long before the person was not meeting expectations. If you set clear expectations and involve the person who needs to meet those expectations in setting them, then there is a clear plan to follow. If you have been checking in with the person and empowering them to either seek assistance as necessary or provide updates as the project or plan progressed, then they should know if they are not meeting those expectations. As to the psychosocial aspects of communicating, there is always the opportunity to set expectations for yourself in giving feedback and in maintaining the work environment that you want for your team. That is at least as much on you as the leader as it is on them as the direct report or team member who is receiving the feedback.
Documentation throughout a timeline and specific examples of missed expectations along with ways to improve are generally helpful. If there was no clear path in place before, a conversation should be had to set/share those expectations and design a path as soon as possible. As a new leader, one of the biggest changes is in managing relationships with others, but there is a wealth of training and resources available to assist with how to do this.
I have been in teams where we shared our preferred communication styles so that we were all better prepared to collaborate. I have been in teams that held regular touchpoint meetings or used other apps or trackers to monitor the progression of plans/projects with all members taking responsibility for their portions and helping meet the timeline.
I was often the kid in high school that felt that group projects just meant that other people benefitted from my work, so I recognize that some people intentionally or indirectly skate by on responsibilities. As a leader, I like to build rapport and an environment of collaboration. There are going to be times when I need assistance or cannot complete a task in the time provided. There are going to be other times when I may be able to provide support or assist others. Communicating those changes and making sure that they are the exception rather than the norm allows me to continually reflect on expectations and work within a professional team.
This is an excellent question. Are you a supervisor or manager?Is this person someone you evaluate? Meeting expectations according to guidelines or job description?
Here is a suggestion: Check to see if you have an Employee Assistance Program (EAP). Did you know EAP assists with supervisor, manager and team building questions. They even have "life coach" type assistance. Inquire with your Human Resource department.