Having had chickenpox won't improve your immunity to MPX, as they are different diseases.
The virus causing Chicken Pox is varicella zoster virus (VZV), a type of herpes virus. If your immune system is down, this virus might reappear as shingles.
Monkeypox however are caused by an infection by the monkeypox virus, which is related to other orthopoxviruses such as smallpox and cowpox.
A prior smallpox vaccination does appear to grant a small bit of immunity against MPX. It's recommended to get a booster with Imvanex (Jynneos), a third generation smallpox vaccine that's rarer than hen's teeth at the moment.