My mother, my sister (neither of whom are/were believers), my wife (who is a believer), and numerous others I've known over the years had what we've all defined as premonitions.
Those which were in regard to me, were feelings of impending danger.
My sister had one once that dealt with a recurrence of cancer-- mine.
As I was a trouble-some boy in my youth, apparently my mom had them quite frequently.
I think for a follower of Jesus, it's important that we pray when we get them.
I've had them off and on over the years, where a name would come to mind, with an uncomfortable feeling. Nothing more. When they first began, there was a name which came to mind, and it stayed with me for a year or more. There were times when the name would carry a melody with it.... it was quite strange, but during this time I was so bothered with it, that I began to pray, I think more to silence the feeling, than to help someone in need. But, it worked.... after several years, I began to realize that when I get these names out of seemingly nowhere, I need to pray for them. Now it's a regular habit. I depend on God to remind me to pray for people who are in need.
I think it may depend on what is meant by "premonition". There are certainly examples of angels communicating through dreams or visions such as these for Joseph and the magi:
. . . an Angel of the Lord appeared to him in his sleep, saying: “Joseph, son of David, do not be afraid to accept Mary as your wife. For what has been formed in her is of the Holy Spirit. Matthew 1:20
And having received a response in sleep that they should not return to Herod, they went back by another way to their own region.
And after they had gone away, behold, an Angel of the Lord appeared in sleep to Joseph, saying: “Rise up, and take the boy and his mother, and flee into Egypt. . . Matthew 2:12-13