Are there any noona romance dramas where the female lead chases the male lead first. because mostly in noona dramas its shown that the ML falls first and pursues the FL. i think they mostly prefer this route, especially if there's a huge age gap or if the ML is 19-23 age range so that it doesn't look like grooming.

But ML could be older. like ML is 30 FL is 40. something like that. but is there any show like that where it has older female younger male romance with the FL approaching the ML?

The Only You - older FL chases the younger ML.

Female CEO Love Me has the FL pursuing the ML who seems to be younger than she is (they're a year apart in real life but in the drama I got the impression that the age gap was wider).

And close but not quite...Destined to Meet You - the ML falls first years before but loses his memory of that. In the present day, the FL approaches the ML first.

Maybe:

 Ichika Kaneki:
But ML could be older. like ML is 30 FL is 40. something like that. but is there any show like that where it has older female younger male romance with the FL approaching the ML?

Not 100% on point, but maybe check out The K2.  The ML and FL are close in age, with the ML being a little older. The FL is the ML's main romantic interest in the drama and they end up together. However, the SFL is a fair bit older than the ML (the SFL actress is 15 years older than the ML actor). She flirts with the ML, there's romantic tension between them for a significant portion of the drama, and many viewers wanted the ML to end up with her instead of the FL

Be With You (Second couple)

My Name is Kim Sam Soon

Pursuit of Happiness They both chase each other, so mutual love. They are like the second leads of other dramas so its an interesting experience and don't let the mutual love part hold you back because its not like your typical noona romances where the Fl holds back because the ml is youngers, and he is the one doing the chasing but more like he isn't the one she is supposed to be in love with.

My Queen ML Does the chasing, FL gets him to sleep with her first LOL.

Long Vacation

Love's Relativity Again similar to Pursuit of Happiness, but in this one ML does the chasing but she falls first.

Not sure if your still checking this thread but a screwed up version of this story line is Misbehavior (Movie) not sure if I should recommend this but it is a older female who loves the male lead but in a batshit crazy way