Work around him. Don't complain about subjective things until you have a better sense of the office politics and relationships involved, if even then.
If you expect are going to miss a deadline and it's because of not getting support from consultant then tell your supervisor and ask how to handle it.

Help! I joined a new team within a company I have been with for several years. I am an IC. I interviewed for the role. I was told that I was being brought on as an add on. It turns out that the group had a recent round of layoffs prior to me joining and one of the people laid off is staying on as a consultant to help me transition. Well, it's been a month and this consultant ex employee is absolute deadweight. It is making me work more to have this guy here. He is not responsive on Teams or email. If anything, he confuses me. Anytime I try to give him work, he says he is going beyond his hours. How the heck do I approach this? My manager seems to really like him.