Grammar practice is important, even though formal grammar study may not be. Grammar is the skeleton of a language. It's the framework that holds words and phrases together in a way that expresses meaning.
Researchers have found that our minds can figure out the grammar of a language just by hearing enough of it. Formal teaching is not necessary, though it speeds up the process. We do need practice if we want to use a new language, though!
EnglishHints has a variety of grammar practice pages. Their purpose to help you use English the way English speakers do.
Much of this practice is available in two forms. You can study them here, or download pdf worksheets. (See English Grammar Worksheets.)
(Some of the practice pages have explanations before the exercise. Others link to the most relevant explanation.)
There are several pages to practice irregular past tense verbs. Their varied forms make them difficult to learning.
Several of these are also printable pdfs on the English Grammar Worksheets page.
(If you can read intermediate-level English, you can also review English tenses in some of our reading and vocabulary exercises. See the gap-fill exercises at the bottom of TOEFL & IELTS Vocabulary. Especially try Disaster Assistance Vocabulary Exercises and Conservation Terminology.)
These pages discuss word formation, but they also show how to use different parts of speech. That’s important, because if you use a noun where a verb should be (or vice versa) you may confuse your hearers.
Practice with phrasal verbs (two or three-word verbs like 'look for') on Phrasal Verb Quiz.
Ivy Panda has a list of social media or YouTube sites for English grammar practice. (I know several, including the British Council and English Club, are very helpful. I'm not familiar with some of the others. )