I am right handed and my cursive used to really suck, but guess what It’s called penmanship, you get a book, like perhaps a calligraphy book and you practice. Your handwriting improves.
Good idea about getting a handwriting book. Maybe it’s not too late to improve it. It’s worth a try!
I took a calligraphy course last year at a local college as an elective toward a Visual Arts degree. There were students whose handwriting was so horrific I seriously wondered if there was any hope for them. By the end of the semester they were producing beautiful work. Amazing.
For someone who merely wanted to improve common printing or cursive it really wouldn't take much time or practice.